Advanced Analytics Statistics

Tests of the Advanced Analytics statistical methods: distributions, hypothesis tests, correlation, regression diagnostics and the numerical building blocks behind the semantic statistics tools.

General

CategoricalAndSurvivalClassifierToolsTests

Jube.Test.AdvancedAnalytics.Statistics.CategoricalAndSurvivalClassifierToolsTests — 57 tests.

Test	Kind	Verifies
CalculateBinaryClassificationMetricsFromCounts_MatchesHandComputation	Fact	Calculate binary classification metrics from counts matches hand computation.
CalculateBinaryClassificationMetricsFromCounts_FBetaFollowsBeta	Fact	Calculate binary classification metrics from counts f beta follows beta.
CalculateBinaryClassificationMetricsFromCounts_DegenerateAndInvalidInputs	Fact	Calculate binary classification metrics from counts degenerate and invalid inputs.
CalculateBinaryClassificationMetricsFromLabels_CountsTheConfusionMatrix	Fact	Calculate binary classification metrics from labels counts the confusion matrix.
CalculateBinaryClassificationMetricsFromLabels_RejectsBadFlags	Fact	Calculate binary classification metrics from labels rejects bad flags.
CalculateBinaryClassificationMetricsAtThreshold_ThresholdIsInclusiveAndNaNIsDropped	Fact	Calculate binary classification metrics at threshold threshold is inclusive and na n is dropped.
CalculateBinaryClassificationMetricsAtThreshold_RejectsNaNThresholdAndAllNaNScores	Fact	Calculate binary classification metrics at threshold rejects na n threshold and all na n scores.
CalculateMulticlassClassificationMetrics_MatchesWikipediaCatsDogsRabbits	Fact	Calculate multiclass classification metrics matches wikipedia cats dogs rabbits.
CalculateMulticlassClassificationMetrics_WeightedKappaClassOrderAndErrors	Fact	Calculate multiclass classification metrics weighted kappa class order and errors.
CalculateMulticlassMetricsFromConfusionMatrix_MatchesLabelsVersion	Fact	Calculate multiclass metrics from confusion matrix matches labels version.
CalculateMulticlassMetricsFromConfusionMatrix_RejectsNonSquareAndFractionalCounts	Fact	Calculate multiclass metrics from confusion matrix rejects non square and fractional counts.
ComputeRocCurve_AucIsRankProbabilityByHand	Fact	Compute roc curve auc is rank probability by hand.
ComputeRocCurve_ThinsPointsDropsNaNAndRejectsSingleClass	Fact	Compute roc curve thins points drops na n and rejects single class.
ComputeRocCurve_TiedScoresGiveHalfCredit	Fact	Compute roc curve tied scores give half credit.
ComparePairedRocAucDelong_InvertedScoreHasMirroredAucAndDoubleStandardError	Fact	Compare paired roc auc delong inverted score has mirrored auc and double standard error.
ComparePairedRocAucDelong_IdenticalScoresHaveNoDifference	Fact	Compare paired roc auc delong identical scores have no difference.
ComputePrecisionRecallCurve_AveragePrecisionMatchesHandComputation	Fact	Compute precision recall curve average precision matches hand computation.
ComputePrecisionRecallCurve_RejectsNoPositives	Fact	Compute precision recall curve rejects no positives.
ComputeLiftGainTable_MatchesHandComputedQuintiles	Fact	Compute lift gain table matches hand computed quintiles.
ComputeLiftGainTable_UnevenGroupSizesAndInvalidGroupCounts	Fact	Compute lift gain table uneven group sizes and invalid group counts.
ComputeKolmogorovSmirnovSeparation_MatchesHandComputation	Fact	Compute kolmogorov smirnov separation matches hand computation.
ComputeKolmogorovSmirnovSeparation_PerfectSeparationIsOneAndSingleClassIsRejected	Fact	Compute kolmogorov smirnov separation perfect separation is one and single class is rejected.
ComputeThresholdSweep_ExplicitThresholdsMatchHandCounts	Fact	Compute threshold sweep explicit thresholds match hand counts.
ComputeThresholdSweep_AutomaticThresholdsAreCappedAndThresholdAboveMaxFlagsNothing	Fact	Compute threshold sweep automatic thresholds are capped and threshold above max flags nothing.
SelectThresholdMaximisingFBeta_PicksHandComputedOptimum	Fact	Select threshold maximising f beta picks hand computed optimum.
SelectThresholdMaximisingFBeta_RejectsBadBetaAndSingleClass	Fact	Select threshold maximising f beta rejects bad beta and single class.
SelectThresholdMaximisingYoudenIndex_TiesChooseTheHighestThreshold	Fact	Select threshold maximising youden index ties choose the highest threshold.
SelectThresholdMaximisingYoudenIndex_PerfectSeparationGivesOne	Fact	Select threshold maximising youden index perfect separation gives one.
SelectThresholdMaximisingMatthewsCorrelation_PicksHandComputedOptimum	Fact	Select threshold maximising matthews correlation picks hand computed optimum.
SelectThresholdMaximisingMatthewsCorrelation_InvertedScoreStillReturnsBestAvailable	Fact	Select threshold maximising matthews correlation inverted score still returns best available.
SelectThresholdMinimisingCost_MatchesHandComputedMinimum	Fact	Select threshold minimising cost matches hand computed minimum.
SelectThresholdMinimisingCost_FlaggingNothingCanBeCheapestAndBadCostsAreRejected	Fact	Select threshold minimising cost flagging nothing can be cheapest and bad costs are rejected.
SelectThresholdForTargetRecall_ReturnsFewestAlertsReachingTarget	Fact	Select threshold for target recall returns fewest alerts reaching target.
SelectThresholdForTargetRecall_FullRecallAndInvalidTargets	Fact	Select threshold for target recall full recall and invalid targets.
SelectThresholdForTargetPrecision_ReturnsLowestThresholdKeepingPrecision	Fact	Select threshold for target precision returns lowest threshold keeping precision.
SelectThresholdForTargetPrecision_UnreachableTargetIsFlagged	Fact	Select threshold for target precision unreachable target is flagged.
SelectThresholdForAlertBudget_UsesLargestQueueWithinBudget	Fact	Select threshold for alert budget uses largest queue within budget.
SelectThresholdForAlertBudget_TiesOverBudgetAndInvalidArguments	Fact	Select threshold for alert budget ties over budget and invalid arguments.
EvaluateTopKAlertQueue_MatchesHandComputedQueues	Fact	Evaluate top k alert queue matches hand computed queues.
EvaluateTopKAlertQueue_RejectsOversizedQueuesAndHandlesNoEvents	Fact	Evaluate top k alert queue rejects oversized queues and handles no events.
CalculateOneVersusRestMulticlassAuc_PerfectAndReversedModels	Fact	Calculate one versus rest multiclass auc perfect and reversed models.
CalculateOneVersusRestMulticlassAuc_AbsentClassIsNaNAndUnknownLabelIsRejected	Fact	Calculate one versus rest multiclass auc absent class is na n and unknown label is rejected.
ComputeCalibrationCurve_EqualCountBinsMatchHandComputation	Fact	Compute calibration curve equal count bins match hand computation.
ComputeCalibrationCurve_UniformBinsAgreeWithSharedExpectedCalibrationError	Fact	Compute calibration curve uniform bins agree with shared expected calibration error.
ComputeCalibrationCurve_RejectsProbabilitiesOutsideUnitInterval	Fact	Compute calibration curve rejects probabilities outside unit interval.
CalculateBrierScoreDecomposition_SatisfiesMurphyIdentity	Fact	Calculate brier score decomposition satisfies murphy identity.
CalculateBrierScoreDecomposition_SingleBinReliabilityIsSquaredMeanGap	Fact	Calculate brier score decomposition single bin reliability is squared mean gap.
CalculateProbabilityScoringRules_MatchesHandComputedBrierAndLogLoss	Fact	Calculate probability scoring rules matches hand computed brier and log loss.
CalculateProbabilityScoringRules_ConfidentWrongPredictionIsClippedAndBadEpsilonRejected	Fact	Calculate probability scoring rules confident wrong prediction is clipped and bad epsilon rejected.
TestHosmerLemeshowCalibration_MatchesHandComputedStatistic	Fact	Test hosmer lemeshow calibration matches hand computed statistic.
TestHosmerLemeshowCalibration_RejectsTooFewGroupsAndGrosslyMiscalibratedIsSignificant	Fact	Test hosmer lemeshow calibration rejects too few groups and grossly miscalibrated is significant.
FitCalibrationSlopeAndIntercept_PerfectlyCalibratedProbabilitiesGiveSlopeNearOne	Fact	Fit calibration slope and intercept perfectly calibrated probabilities give slope near one.
FitCalibrationSlopeAndIntercept_OverConfidentProbabilitiesHaveSmallSlope	Fact	Fit calibration slope and intercept over confident probabilities have small slope.
CalculateMulticlassLogLoss_MatchesHandComputation	Fact	Calculate multiclass log loss matches hand computation.
CalculateMulticlassLogLoss_RejectsUnknownClassNegativeAndAllNaN	Fact	Calculate multiclass log loss rejects unknown class negative and all na n.
AdjustProbabilitiesForBaseRate_ShiftsLogOddsByTheBaseRateDifference	Fact	Adjust probabilities for base rate shifts log odds by the base rate difference.
AdjustProbabilitiesForBaseRate_RejectsInvalidRatesAndProbabilities	Fact	Adjust probabilities for base rate rejects invalid rates and probabilities.

CategoricalAndSurvivalSurvivalToolsTests

Jube.Test.AdvancedAnalytics.Statistics.CategoricalAndSurvivalSurvivalToolsTests — 38 tests.

Test	Kind	Verifies
EstimateKaplanMeierSurvival_MatchesFreireichSixMercaptopurineCurve	Fact	Estimate kaplan meier survival matches freireich six mercaptopurine curve.
EstimateKaplanMeierSurvival_PlateauAtHalfTakesTheMidpointAndQuartilesFollow	Fact	Estimate kaplan meier survival plateau at half takes the midpoint and quartiles follow.
EstimateKaplanMeierSurvival_HandlesCensoringOnlyNaNAndInvalidInput	Fact	Estimate kaplan meier survival handles censoring only na n and invalid input.
EstimateKaplanMeierSurvival_ConfidenceMethodsOrderAsExpected	Fact	Estimate kaplan meier survival confidence methods order as expected.
EstimateKaplanMeierByGroup_MatchesFreireichMediansAndLogRank	Fact	Estimate kaplan meier by group matches freireich medians and log rank.
EstimateKaplanMeierByGroup_SingleGroupHasNoLogRankAndBlankGroupsAreDropped	Fact	Estimate kaplan meier by group single group has no log rank and blank groups are dropped.
EstimateNelsonAalenCumulativeHazard_MatchesHarmonicSumsByHand	Fact	Estimate nelson aalen cumulative hazard matches harmonic sums by hand.
EstimateNelsonAalenCumulativeHazard_TiesAndCensoringAreCountedAtRisk	Fact	Estimate nelson aalen cumulative hazard ties and censoring are counted at risk.
EvaluateSurvivalAtTimes_ReadsTheStepFunctionAtRequestedTimes	Fact	Evaluate survival at times reads the step function at requested times.
EvaluateSurvivalAtTimes_RequiresAtLeastOneValidTime	Fact	Evaluate survival at times requires at least one valid time.
CalculateSurvivalTimeQuantiles_ReturnsMedianAndQuartilesWithBrookmeyerCrowleyLimits	Fact	Calculate survival time quantiles returns median and quartiles with brookmeyer crowley limits.
CalculateSurvivalTimeQuantiles_UnreachableQuantileIsNaNAndBadProportionsRejected	Fact	Calculate survival time quantiles unreachable quantile is na n and bad proportions rejected.
CalculateRestrictedMeanSurvivalTime_MatchesAreaUnderTheStepCurveByHand	Fact	Calculate restricted mean survival time matches area under the step curve by hand.
CalculateRestrictedMeanSurvivalTime_HorizonBeyondFollowUpIsFlaggedAndInvalidHorizonRejected	Fact	Calculate restricted mean survival time horizon beyond follow up is flagged and invalid horizon rejected.
CompareRestrictedMeanSurvivalTime_MatchesHandComputedDifferenceAndZ	Fact	Compare restricted mean survival time matches hand computed difference and z.
CompareRestrictedMeanSurvivalTime_RequiresExactlyTwoGroups	Fact	Compare restricted mean survival time requires exactly two groups.
EstimateMedianFollowUpTime_ReversesTheRolesOfEventsAndCensoring	Fact	Estimate median follow up time reverses the roles of events and censoring.
EstimateMedianFollowUpTime_NoCensoringMeansNoReverseMedian	Fact	Estimate median follow up time no censoring means no reverse median.
TestLogRankSurvivalDifference_MatchesFreireichObservedAndExpectedCounts	Fact	Test log rank survival difference matches freireich observed and expected counts.
TestLogRankSurvivalDifference_WeightedStatisticsMatchHandComputedInterleavedSample	Theory	Test log rank survival difference weighted statistics match hand computed interleaved sample.
TestLogRankSurvivalDifference_FlemingHarringtonReducesToLogRankAndTargetsEarlyOrLate	Fact	Test log rank survival difference fleming harrington reduces to log rank and targets early or late.
TestLogRankSurvivalDifference_ThreeIdenticalGroupsGiveZeroChiSquareOnTwoDegrees	Fact	Test log rank survival difference three identical groups give zero chi square on two degrees.
FitCoxProportionalHazards_MatchesBreslowSolutionForFreireichLeukaemiaData	Fact	Fit cox proportional hazards matches breslow solution for freireich leukaemia data.
FitCoxProportionalHazards_PredictionsFollowTheProportionalHazardsIdentity	Fact	Fit cox proportional hazards predictions follow the proportional hazards identity.
FitCoxProportionalHazards_RejectsBadInputAndWarnsOnFewEvents	Fact	Fit cox proportional hazards rejects bad input and warns on few events.
FitCoxProportionalHazards_IsInvariantToTimeUnitsAndDropsIncompleteRows	Fact	Fit cox proportional hazards is invariant to time units and drops incomplete rows.
CalculateHarrellConcordanceIndex_PerfectReversedAndConstantRankings	Fact	Calculate harrell concordance index perfect reversed and constant rankings.
CalculateHarrellConcordanceIndex_CensoredShorterCasesAreNotComparable	Fact	Calculate harrell concordance index censored shorter cases are not comparable.
FitExponentialSurvivalModel_MatchesClosedFormMaximumLikelihood	Fact	Fit exponential survival model matches closed form maximum likelihood.
FitExponentialSurvivalModel_NoEventsAndZeroTimeAreHandled	Fact	Fit exponential survival model no events and zero time are handled.
CalculateIncidenceRatesByGroup_MatchesPersonTimeRatesAndExactRatio	Fact	Calculate incidence rates by group matches person time rates and exact ratio.
CalculateIncidenceRatesByGroup_UnknownReferenceAndZeroPersonTime	Fact	Calculate incidence rates by group unknown reference and zero person time.
TabulateHazardRateByInterval_MatchesHandComputedPersonTime	Fact	Tabulate hazard rate by interval matches hand computed person time.
TabulateHazardRateByInterval_RejectsBadBreaks	Fact	Tabulate hazard rate by interval rejects bad breaks.
BuildActuarialLifeTable_MatchesHandComputedIntervals	Fact	Build actuarial life table matches hand computed intervals.
BuildActuarialLifeTable_EmptyIntervalsCarrySurvivalForward	Fact	Build actuarial life table empty intervals carry survival forward.
CalculateCumulativeIncidenceCompetingRisks_MatchesAalenJohansenByHand	Fact	Calculate cumulative incidence competing risks matches aalen johansen by hand.
CalculateCumulativeIncidenceCompetingRisks_RejectsNegativeCodesAndNoEvents	Fact	Calculate cumulative incidence competing risks rejects negative codes and no events.

CategoricalAndSurvivalToolsTests

Jube.Test.AdvancedAnalytics.Statistics.CategoricalAndSurvivalToolsTests — 58 tests.

Test	Kind	Verifies
CrossTabulateCategories_CountsCellsAndSkipsBlankLabels	Fact	Cross tabulate categories counts cells and skips blank labels.
CrossTabulateCategories_RejectsMismatchedLengthsAndAllBlank	Fact	Cross tabulate categories rejects mismatched lengths and all blank.
AnalyseContingencyTableAssociation_TwoByTwoMatchesHandComputation	Fact	Analyse contingency table association two by two matches hand computation.
AnalyseContingencyTableAssociation_MatchesAgrestiPartyIdentificationTable	Fact	Analyse contingency table association matches agresti party identification table.
AnalyseContingencyTableAssociation_RejectsBadTablesAndWarnsOnSparseCells	Fact	Analyse contingency table association rejects bad tables and warns on sparse cells.
AnalyseContingencyTableAssociation_HugeCountsRemainFinite	Fact	Analyse contingency table association huge counts remain finite.
AnalyseCategoricalAssociationFromLabels_CrossTabulatesThenAnalyses	Fact	Analyse categorical association from labels cross tabulates then analyses.
AnalyseCategoricalAssociationFromLabels_ConstantVariableIsRejected	Fact	Analyse categorical association from labels constant variable is rejected.
RankCategoricalColumnsByAssociationWithOutcome_RanksInformativeColumnAboveNoise	Fact	Rank categorical columns by association with outcome ranks informative column above noise.
RankCategoricalColumnsByAssociationWithOutcome_RejectsRaggedRowsDuplicateNamesAndSingleClassOutcome	Fact	Rank categorical columns by association with outcome rejects ragged rows duplicate names and single class outcome.
CalculateGoodmanKruskalLambda_MatchesHandComputation	Fact	Calculate goodman kruskal lambda matches hand computation.
CalculateGoodmanKruskalLambda_IndependenceIsZeroAndDegenerateIsNaN	Fact	Calculate goodman kruskal lambda independence is zero and degenerate is na n.
CalculateOrdinalAssociationMeasures_MatchesAgrestiJobSatisfactionGamma	Fact	Calculate ordinal association measures matches agresti job satisfaction gamma.
CalculateOrdinalAssociationMeasures_TwoByTwoReducesToYuleQAndPhi	Fact	Calculate ordinal association measures two by two reduces to yule q and phi.
CalculateOrdinalAssociationMeasures_ReversedOrderIsNegativeOne	Fact	Calculate ordinal association measures reversed order is negative one.
CalculateCategoricalMutualInformation_PerfectDependenceIsOneBit	Fact	Calculate categorical mutual information perfect dependence is one bit.
CalculateOddsRatio_MatchesWoolfIntervalByHand	Fact	Calculate odds ratio matches woolf interval by hand.
CalculateOddsRatio_ZeroCellUsesHaldaneCorrectionOnlyWhenAsked	Fact	Calculate odds ratio zero cell uses haldane correction only when asked.
CalculateOddsRatio_RejectsBadInput	Fact	Calculate odds ratio rejects bad input.
CalculateRiskRatio_MatchesPhysiciansHealthStudyAspirinTrial	Fact	Calculate risk ratio matches physicians health study aspirin trial.
CalculateRiskRatio_ZeroEventGroupIsCorrectedAndFlagged	Fact	Calculate risk ratio zero event group is corrected and flagged.
CalculateRiskDifference_MatchesNewcombe1998ScoreIntervalExample	Fact	Calculate risk difference matches newcombe1998 score interval example.
CalculateRiskDifference_IdenticalRatesGiveZeroDifference	Fact	Calculate risk difference identical rates give zero difference.
CalculateNumberNeededToTreat_InvertsTheRiskDifference	Fact	Calculate number needed to treat inverts the risk difference.
CalculateNumberNeededToTreat_NoDifferenceHasNoFiniteNumber	Fact	Calculate number needed to treat no difference has no finite number.
CalculateYuleAssociation_MatchesClosedForms	Fact	Calculate yule association matches closed forms.
CalculateYuleAssociation_EmptyOffDiagonalGivesPerfectAssociationAndNaNStandardError	Fact	Calculate yule association empty off diagonal gives perfect association and na n standard error.
CalculateDiagnosticLikelihoodRatios_MatchesBayesByHand	Fact	Calculate diagnostic likelihood ratios matches bayes by hand.
CalculateDiagnosticLikelihoodRatios_DefaultsPretestToPrevalenceAndRejectsBadPretest	Fact	Calculate diagnostic likelihood ratios defaults pretest to prevalence and rejects bad pretest.
AnalyseTwoByTwoTable_CombinesEveryMeasure	Fact	Analyse two by two table combines every measure.
AnalyseTwoByTwoTable_RejectsEmptyEventColumn	Fact	Analyse two by two table rejects empty event column.
AnalyseBinaryExposureAndOutcome_BuildsTheTableFromFlags	Fact	Analyse binary exposure and outcome builds the table from flags.
AnalyseBinaryExposureAndOutcome_RejectsNonBinaryAndMismatched	Fact	Analyse binary exposure and outcome rejects non binary and mismatched.
CalculateMantelHaenszelOddsRatio_SingleStratumMatchesHandComputation	Fact	Calculate mantel haenszel odds ratio single stratum matches hand computation.
CalculateMantelHaenszelOddsRatio_IdenticalStrataAreHomogeneousAndHeterogeneousOnesAreNot	Fact	Calculate mantel haenszel odds ratio identical strata are homogeneous and heterogeneous ones are not.
CalculateMantelHaenszelOddsRatio_RejectsMalformedStrata	Fact	Calculate mantel haenszel odds ratio rejects malformed strata.
CalculateBinomialProportionConfidenceInterval_MatchesPublishedEightOfTenIntervals	Theory	Calculate binomial proportion confidence interval matches published eight of ten intervals.
CalculateBinomialProportionConfidenceInterval_WaldIsClippedAndEdgesAreHandled	Fact	Calculate binomial proportion confidence interval wald is clipped and edges are handled.
CalculateInformationValueByCategory_MatchesClosedFormWeightOfEvidence	Fact	Calculate information value by category matches closed form weight of evidence.
CalculateInformationValueByCategory_ZeroCellIsSmoothedAndBlankIsSkipped	Fact	Calculate information value by category zero cell is smoothed and blank is skipped.
CalculateInformationValueByBins_SeparatedHalvesMatchSmoothedClosedForm	Fact	Calculate information value by bins separated halves match smoothed closed form.
CalculateInformationValueByBins_MissingValuesFormTheirOwnBin	Fact	Calculate information value by bins missing values form their own bin.
CalculatePopulationStabilityIndexFromCounts_MatchesHandComputation	Fact	Calculate population stability index from counts matches hand computation.
CalculatePopulationStabilityIndexFromCounts_RejectsBadInput	Fact	Calculate population stability index from counts rejects bad input.
CalculatePopulationStabilityIndexForNumericValues_IdenticalSamplesAreStableAndShiftedOnesAreNot	Fact	Calculate population stability index for numeric values identical samples are stable and shifted ones are not.
CalculatePopulationStabilityIndexForNumericValues_MissingBinAndEmptyBaseline	Fact	Calculate population stability index for numeric values missing bin and empty baseline.
CalculatePopulationStabilityIndexForCategories_MatchesCountsVersion	Fact	Calculate population stability index for categories matches counts version.
CalculatePopulationStabilityIndexForCategories_NewCategoryAppearsAsBin	Fact	Calculate population stability index for categories new category appears as bin.
TabulateEventRateBySegment_MatchesHandComputedRatesLiftAndHomogeneity	Fact	Tabulate event rate by segment matches hand computed rates lift and homogeneity.
TabulateEventRateBySegment_FlagsSmallSamplesAndHandlesNoEvents	Fact	Tabulate event rate by segment flags small samples and handles no events.
TabulateAlertHitRatesBySegment_ComputesAlertHitAndDetectionRates	Fact	Tabulate alert hit rates by segment computes alert hit and detection rates.
TabulateAlertHitRatesBySegment_NoAlertsGiveZeroHitRateAndRejectsBadFlags	Fact	Tabulate alert hit rates by segment no alerts give zero hit rate and rejects bad flags.
CalculatePoissonRateConfidenceInterval_MatchesExactGarwoodLimits	Fact	Calculate poisson rate confidence interval matches exact garwood limits.
CalculatePoissonRateConfidenceInterval_RejectsBadInput	Fact	Calculate poisson rate confidence interval rejects bad input.
ComparePoissonRates_MatchesExactBinomialByHand	Fact	Compare poisson rates matches exact binomial by hand.
ComparePoissonRates_ZeroEventGroupsAreHandled	Fact	Compare poisson rates zero event groups are handled.
TestPoissonDispersion_MatchesChiSquareClosedFormForTwoDegreesOfFreedom	Fact	Test poisson dispersion matches chi square closed form for two degrees of freedom.
TestPoissonDispersion_BurstyCountsAreOverdispersedAndZerosAreUntestable	Fact	Test poisson dispersion bursty counts are overdispersed and zeros are untestable.

DataPreparationAndResamplingToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DataPreparationAndResamplingToolsTests — 134 tests.

Test	Kind	Verifies
FitLabelEncoderSortedCodesAndMissingIsMinusOne	Fact	Fit label encoder sorted codes and missing is minus one.
FitLabelEncoderFirstAppearanceAndFrequencyOrders	Fact	Fit label encoder first appearance and frequency orders.
ApplyLabelEncoderUsesGivenRankOrderAndUnknownCode	Fact	Apply label encoder uses given rank order and unknown code.
FitOneHotEncoderProducesOneColumnPerCategory	Fact	Fit one hot encoder produces one column per category.
FitOneHotEncoderRefusesExplosiveCardinality	Fact	Fit one hot encoder refuses explosive cardinality.
ApplyOneHotEncoderUnseenCategoryIsAllZeros	Fact	Apply one hot encoder unseen category is all zeros.
FitTargetMeanEncoderShrinksTowardsTheOverallRate	Fact	Fit target mean encoder shrinks towards the overall rate.
FitTargetMeanEncoderRejectsBadLabelsAndNegativeSmoothing	Fact	Fit target mean encoder rejects bad labels and negative smoothing.
FitWeightOfEvidenceIsLogRatioOfEventToNonEventShares	Fact	Fit weight of evidence is log ratio of event to non event shares.
FitWeightOfEvidenceSmoothingKeepsEmptyCellsFiniteAndSingleClassIsRejected	Fact	Fit weight of evidence smoothing keeps empty cells finite and single class is rejected.
FitFrequencyEncoderReturnsFractionsOrCounts	Fact	Fit frequency encoder returns fractions or counts.
ApplyCategoryEncoderMapsKnownAndFallsBackToDefault	Fact	Apply category encoder maps known and falls back to default.
FitRareCategoryGroupingReplacesRareLevelsWithOther	Fact	Fit rare category grouping replaces rare levels with other.
ApplyRareCategoryGroupingMapsUnseenToOther	Fact	Apply rare category grouping maps unseen to other.
DiscretiseEqualWidthCutsRangeIntoEqualIntervals	Fact	Discretise equal width cuts range into equal intervals.
DiscretiseEqualWidthWithLabelsAddsEventStatisticsAndHandlesMissingAndConstant	Fact	Discretise equal width with labels adds event statistics and handles missing and constant.
DiscretiseEqualFrequencyCutsAtQuantilesGivingEqualCounts	Fact	Discretise equal frequency cuts at quantiles giving equal counts.
DiscretiseEqualFrequencyMergesTiedCutPoints	Fact	Discretise equal frequency merges tied cut points.
DiscretiseKMeansSeparatesThreeClumps	Fact	Discretise k means separates three clumps.
DiscretiseKMeansWithFewDistinctValuesReducesBins	Fact	Discretise k means with few distinct values reduces bins.
DiscretiseSupervisedFindsTheCutWhereTheEventRateJumps	Fact	Discretise supervised finds the cut where the event rate jumps.
DiscretiseSupervisedRejectsSingleClassAndTinyBinCount	Fact	Discretise supervised rejects single class and tiny bin count.
DiscretiseCustomEdgesPutsAnEdgeValueInTheLowerBin	Fact	Discretise custom edges puts an edge value in the lower bin.
ApplyBinEdgesAssignsBeyondRangeAndMissing	Fact	Apply bin edges assigns beyond range and missing.
GeneratePolynomialFeaturesDegreeTwoHasPowersAndProduct	Fact	Generate polynomial features degree two has powers and product.
GeneratePolynomialFeaturesDegreeThreeCountsAndLimit	Fact	Generate polynomial features degree three counts and limit.
GenerateColumnPairFeaturesRatioDifferenceAndUndefinedCounts	Fact	Generate column pair features ratio difference and undefined counts.
GenerateLagFeaturesShiftsAndDifferences	Fact	Generate lag features shifts and differences.
GenerateLagFeaturesWithinGroupsAndRollingWindowExcludesCurrentRow	Fact	Generate lag features within groups and rolling window excludes current row.
ExtractDateTimePartsForAKnownDate	Fact	Extract date time parts for a known date.
ExtractDateTimePartsOffsetWeekendMonthEndAndUnparsed	Fact	Extract date time parts offset weekend month end and unparsed.
ExtractEpochPartsSecondsMillisecondsAndInvalid	Fact	Extract epoch parts seconds milliseconds and invalid.
ComputeElapsedTimeInDifferentUnits	Fact	Compute elapsed time in different units.
EncodeCyclicalFeatureMakesTheEndsOfTheCycleNeighbours	Fact	Encode cyclical feature makes the ends of the cycle neighbours.
SelectTableColumnsKeepsAndReordersByName	Fact	Select table columns keeps and reorders by name.
SelectByVarianceThresholdDropsConstantAndLowVarianceColumns	Fact	Select by variance threshold drops constant and low variance columns.
FilterCorrelatedFeaturesDropsOneOfAPerfectlyCorrelatedPair	Fact	Filter correlated features drops one of a perfectly correlated pair.
FilterCorrelatedFeaturesKeepsTheMemberMoreCorrelatedWithTheTarget	Fact	Filter correlated features keeps the member more correlated with the target.
RankFeaturesByAnovaFMatchesHandComputedTwoClassAnova	Fact	Rank features by anova f matches hand computed two class anova.
RankFeaturesByAnovaFRejectsSingleClassAndRanksUnusableFeatureLast	Fact	Rank features by anova f rejects single class and ranks unusable feature last.
RankFeaturesByFRegressionMatchesTextbookSimpleRegression	Fact	Rank features by f regression matches textbook simple regression.
RankFeaturesByFRegressionConstantFeatureIsNaN	Fact	Rank features by f regression constant feature is na n.
RankCountFeaturesByChiSquareMatchesHandComputedStatistic	Fact	Rank count features by chi square matches hand computed statistic.
RankCountFeaturesByChiSquareRejectsNegativeValuesAndZeroColumns	Fact	Rank count features by chi square rejects negative values and zero columns.
RankCategoricalFeaturesByChiSquareMatchesTwoByTwoHandComputation	Fact	Rank categorical features by chi square matches two by two hand computation.
RankCategoricalFeaturesByChiSquareRejectsSingleClass	Fact	Rank categorical features by chi square rejects single class.
RankFeaturesByMutualInformationPerfectSeparatorIsLnTwo	Fact	Rank features by mutual information perfect separator is ln two.
RankFeaturesByMutualInformationCapturesInformativeMissingness	Fact	Rank features by mutual information captures informative missingness.
EliminateFeaturesRecursivelyKeepsTheOnlyRealPredictor	Fact	Eliminate features recursively keeps the only real predictor.
EliminateFeaturesRecursivelyValidatesArguments	Fact	Eliminate features recursively validates arguments.
ProfileMissingValuesCountsCellsRowsAndPatterns	Fact	Profile missing values counts cells rows and patterns.
ProfileMissingValuesWarnsAboutEntirelyMissingColumnAndRejectsBadInput	Fact	Profile missing values warns about entirely missing column and rejects bad input.
ImputeMissingValuesMedianReplacesGapsAndReportsThem	Fact	Impute missing values median replaces gaps and reports them.
ImputeMissingValuesMeanModeConstantAndIndicators	Fact	Impute missing values mean mode constant and indicators.
ImputeMissingValuesRejectsAllMissingColumnUnlessConstant	Fact	Impute missing values rejects all missing column unless constant.
ApplyImputerUsesFixedFillValuesAndIndicators	Fact	Apply imputer uses fixed fill values and indicators.
ApplyImputerRejectsWrongNumberOfFillValues	Fact	Apply imputer rejects wrong number of fill values.
ImputeForwardFillCarriesLastValueAndOptionallyBackfillsLeadingGaps	Fact	Impute forward fill carries last value and optionally backfills leading gaps.
ImputeLinearInterpolationFillsInteriorGapsOnALine	Fact	Impute linear interpolation fills interior gaps on a line.
ImputeNearestNeighboursCopiesTheNearestRowsValue	Fact	Impute nearest neighbours copies the nearest rows value.
ImputeNearestNeighboursFallsBackToColumnMeanWithoutOverlapAndRejectsEmptyColumn	Fact	Impute nearest neighbours falls back to column mean without overlap and rejects empty column.
DropSparseRowsAndColumnsRemovesEmptyColumnThenIncompleteRows	Fact	Drop sparse rows and columns removes empty column then incomplete rows.
DropSparseRowsAndColumnsRejectsBadFractions	Fact	Drop sparse rows and columns rejects bad fractions.
FitTableScalerStandardIsZScoreWithSampleStandardDeviation	Fact	Fit table scaler standard is z score with sample standard deviation.
FitTableScalerMinMaxRobustAndMaxAbsMatchDefinitions	Fact	Fit table scaler min max robust and max abs match definitions.
FitTableScalerHandlesConstantMissingAndEmptyColumns	Fact	Fit table scaler handles constant missing and empty columns.
ApplyTableScalerUsesFixedCentersAndScales	Fact	Apply table scaler uses fixed centers and scales.
InvertTableScalerRoundTripsAFittedScaler	Fact	Invert table scaler round trips a fitted scaler.
NormaliseRowsToUnitNormMatchesNormDefinitions	Fact	Normalise rows to unit norm matches norm definitions.
FitQuantileTransformerUniformMapsRanksToUnitInterval	Fact	Fit quantile transformer uniform maps ranks to unit interval.
FitQuantileTransformerTiesShareTheMidRank	Fact	Fit quantile transformer ties share the mid rank.
ApplyQuantileTransformerInterpolatesAndClipsToTheEnds	Fact	Apply quantile transformer interpolates and clips to the ends.
ApplyPowerTransformerMatchesBoxCoxAndYeoJohnsonFormulas	Fact	Apply power transformer matches box cox and yeo johnson formulas.
FitPowerTransformerYeoJohnsonOfSymmetricDataHasLambdaOne	Fact	Fit power transformer yeo johnson of symmetric data has lambda one.
FitPowerTransformerBoxCoxOfLogSymmetricDataIsNearLogarithm	Fact	Fit power transformer box cox of log symmetric data is near logarithm.
FitPowerTransformerRejectsNonPositiveBoxCoxTooFewValuesAndBadRange	Fact	Fit power transformer rejects non positive box cox too few values and bad range.
ApplyColumnFunctionMatchesClosedFormsAndCountsUndefinedCells	Fact	Apply column function matches closed forms and counts undefined cells.
FitOutlierClipperIqrFencesClipTheExtremeValue	Fact	Fit outlier clipper iqr fences clip the extreme value.
FitOutlierClipperQuantileMadAndStandardDeviationBounds	Fact	Fit outlier clipper quantile mad and standard deviation bounds.
FitOutlierClipperRejectsBadQuantilesAndEmptyColumns	Fact	Fit outlier clipper rejects bad quantiles and empty columns.
ApplyOutlierClipperCapsAtFixedBoundsAndKeepsMissing	Fact	Apply outlier clipper caps at fixed bounds and keeps missing.
DescribeDatasetShapeInfersColumnTypes	Fact	Describe dataset shape infers column types.
DescribeDatasetShapeRejectsRaggedTables	Fact	Describe dataset shape rejects ragged tables.
DescribeCategoricalTableProfilesCardinalityAndEntropy	Fact	Describe categorical table profiles cardinality and entropy.
FindDuplicateRowsGroupsRepeatsAndTreatsNaNAsEqual	Fact	Find duplicate rows groups repeats and treats na n as equal.
FindDuplicateCategoricalRowsTreatsNullAndEmptyAlike	Fact	Find duplicate categorical rows treats null and empty alike.
CheckTargetBalanceReportsRatioAndEntropy	Fact	Check target balance reports ratio and entropy.
CheckTargetBalanceWarnsOnSingleAndVeryRareClasses	Fact	Check target balance warns on single and very rare classes.
DataQualityReportFlagsConstantLeakageMissingnessAndDuplicates	Fact	Data quality report flags constant leakage missingness and duplicates.
DataQualityReportFindsPerfectSeparatorAndIdentifierAndValidatesTargets	Fact	Data quality report finds perfect separator and identifier and validates targets.
DataQualityReportOnCleanDataHasNoErrorsAndUsesNumericTarget	Fact	Data quality report on clean data has no errors and uses numeric target.
DataQualityReportCategoricalFlagsFormattingConstantLeakageAndDuplicates	Fact	Data quality report categorical flags formatting constant leakage and duplicates.
DataQualityReportCategoricalFlagsHighCardinalityMissingAndRareCategories	Fact	Data quality report categorical flags high cardinality missing and rare categories.
SampleSimpleRandomWithoutReplacementIsUniqueSortedAndReproducible	Fact	Sample simple random without replacement is unique sorted and reproducible.
SampleSimpleRandomWithReplacementCanExceedPopulationAndRejectsImpossibleDraws	Fact	Sample simple random with replacement can exceed population and rejects impossible draws.
SampleStratifiedProportionalAndEqualAllocation	Fact	Sample stratified proportional and equal allocation.
SampleSystematicHasConstantSpacing	Fact	Sample systematic has constant spacing.
SampleReservoirKeepsKUniqueRowsAndIsRoughlyUniform	Fact	Sample reservoir keeps k unique rows and is roughly uniform.
SampleWeightedNeverPicksZeroWeightAndFavoursHeavyRows	Fact	Sample weighted never picks zero weight and favours heavy rows.
SampleWeightedRejectsBadWeightsAndImpossibleDraws	Fact	Sample weighted rejects bad weights and impossible draws.
SampleClustersReturnsWholeGroups	Fact	Sample clusters returns whole groups.
SplitTrainValidationTestPartitionsRowsInTheRequestedShares	Fact	Split train validation test partitions rows in the requested shares.
SplitTrainValidationTestStratifiesAndValidatesFractions	Fact	Split train validation test stratifies and validates fractions.
SplitByGroupKeepsEveryGroupInOneSet	Fact	Split by group keeps every group in one set.
SplitTimeOrderedPutsTheFutureInTest	Fact	Split time ordered puts the future in test.
SplitTimeOrderedPurgeGapAndValidation	Fact	Split time ordered purge gap and validation.
GenerateKFoldsTestSetsPartitionTheRows	Fact	Generate k folds test sets partition the rows.
GenerateStratifiedKFoldsKeepsClassProportions	Fact	Generate stratified k folds keeps class proportions.
GenerateGroupKFoldsNeverSplitsAGroup	Fact	Generate group k folds never splits a group.
GenerateTimeSeriesFoldsExpandTheTrainingWindow	Fact	Generate time series folds expand the training window.
GenerateLeaveOneOutFoldsTestsOneRowEach	Fact	Generate leave one out folds tests one row each.
GenerateRepeatedKFoldsGivesRepeatsTimesFoldsWithDifferentShuffles	Fact	Generate repeated k folds gives repeats times folds with different shuffles.
GenerateBootstrapSamplesLeaveAboutAThirdOutOfBag	Fact	Generate bootstrap samples leave about a third out of bag.
GeneratePermutationIsAShuffleOfAllIndices	Fact	Generate permutation is a shuffle of all indices.
ComputeClassWeightsBalancedIsNOverClassesTimesCount	Fact	Compute class weights balanced is n over classes times count.
ComputeClassWeightsOtherMethodsAreRescaledToMeanOne	Fact	Compute class weights other methods are rescaled to mean one.
RandomUnderSampleKeepsTheMinorityAndCutsTheMajority	Fact	Random under sample keeps the minority and cuts the majority.
RandomOverSampleKeepsEveryOriginalRowAndRepeatsMinorityRows	Fact	Random over sample keeps every original row and repeats minority rows.
GenerateSmoteSamplesInterpolatesBetweenMinorityNeighbours	Fact	Generate smote samples interpolates between minority neighbours.
GenerateSmoteSamplesRejectsMissingValuesAndTinyMinority	Fact	Generate smote samples rejects missing values and tiny minority.
BootstrapStatisticIntervalOfTheMeanMatchesTheClassicalStandardError	Fact	Bootstrap statistic interval of the mean matches the classical standard error.
BootstrapStatisticIntervalAllMethodsBracketTheEstimate	Fact	Bootstrap statistic interval all methods bracket the estimate.
BootstrapStatisticIntervalStatisticsConstantsAndValidation	Fact	Bootstrap statistic interval statistics constants and validation.
BootstrapTwoSampleDifferenceExcludesZeroForSeparatedSamples	Fact	Bootstrap two sample difference excludes zero for separated samples.
BootstrapCorrelationIntervalOfAPerfectLineIsDegenerate	Fact	Bootstrap correlation interval of a perfect line is degenerate.
BootstrapCorrelationIntervalMatchesTextbookCorrelationAndBracketsIt	Fact	Bootstrap correlation interval matches textbook correlation and brackets it.
JackknifeOfTheMeanHasZeroBiasAndTextbookStandardError	Fact	Jackknife of the mean has zero bias and textbook standard error.
JackknifeOfTheUnbiasedVarianceHasZeroBiasAndValidatesInput	Fact	Jackknife of the unbiased variance has zero bias and validates input.
PermutationTestTwoSampleExactMatchesHandEnumeration	Fact	Permutation test two sample exact matches hand enumeration.
PermutationTestTwoSampleMonteCarloPValueIsBoundedBelowAndOtherStatisticsRun	Fact	Permutation test two sample monte carlo p value is bounded below and other statistics run.
PermutationTestCorrelationExactForPerfectAssociation	Fact	Permutation test correlation exact for perfect association.
PermutationTestCorrelationMonteCarloAndValidation	Fact	Permutation test correlation monte carlo and validation.
PermutationTestPairedExactSignFlipsMatchHandCount	Fact	Permutation test paired exact sign flips match hand count.
PermutationTestPairedMonteCarloAndValidation	Fact	Permutation test paired monte carlo and validation.

DescriptiveStatisticsToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DescriptiveStatisticsToolsTests — 100 tests.

Test	Kind	Verifies
MeanOfTextbookExampleIsFive	Fact	Mean of textbook example is five.
MeanRejectsNaNUnlessIgnoredAndHandlesEmptyAndHugeValues	Fact	Mean rejects na n unless ignored and handles empty and huge values.
WeightedMeanMatchesHandComputation	Fact	Weighted mean matches hand computation.
TrimmedMeanDropsOneValuePerTail	Fact	Trimmed mean drops one value per tail.
WinsorisedMeanReplacesTailsWithNeighbours	Fact	Winsorised mean replaces tails with neighbours.
GeometricMeanIsRootOfProduct	Fact	Geometric mean is root of product.
HarmonicMeanIsCountOverSumOfReciprocals	Fact	Harmonic mean is count over sum of reciprocals.
QuadraticMeanIsRootMeanSquare	Fact	Quadratic mean is root mean square.
PowerMeanRecoversSpecialCases	Fact	Power mean recovers special cases.
ContraharmonicMeanIsSumOfSquaresOverSum	Fact	Contraharmonic mean is sum of squares over sum.
ExponentialWeightedMeanWithFullAlphaIsLastValue	Fact	Exponential weighted mean with full alpha is last value.
GrandMeanWeightsByGroupSize	Fact	Grand mean weights by group size.
MedianAveragesTheMiddlePairForEvenCounts	Fact	Median averages the middle pair for even counts.
TrimeanCombinesQuartilesAndMedian	Fact	Trimean combines quartiles and median.
MidhingeAveragesQuartiles	Fact	Midhinge averages quartiles.
MinimumMaximumRangeReportsExtent	Fact	Minimum maximum range reports extent.
MinimumFindsSmallestAndSkipsMissingWhenAsked	Fact	Minimum finds smallest and skips missing when asked.
MaximumFindsLargest	Fact	Maximum finds largest.
ArgumentOfMinimumReturnsFirstIndexInOriginalArray	Fact	Argument of minimum returns first index in original array.
ArgumentOfMaximumReturnsFirstIndexInOriginalArray	Fact	Argument of maximum returns first index in original array.
SumAddsValues	Fact	Sum adds values.
ProductMultipliesValues	Fact	Product multiplies values.
CountValuesProfilesDataQuality	Fact	Count values profiles data quality.
ModeOfNumbersReturnsEveryTiedMode	Fact	Mode of numbers returns every tied mode.
ModeOfCategoriesReturnsTiedLabels	Fact	Mode of categories returns tied labels.
WeightedModeUsesTotalWeight	Fact	Weighted mode uses total weight.
CircularMeanOfHoursAroundMidnightIsMidnight	Fact	Circular mean of hours around midnight is midnight.
CircularSummaryResultantIsCosineOfHalfSpread	Fact	Circular summary resultant is cosine of half spread.
QuantileFollowsHyndmanFanDefinitions	Fact	Quantile follows hyndman fan definitions.
QuantilesReturnOnePerProbabilityInOrder	Fact	Quantiles return one per probability in order.
PercentilesUsePercentLevels	Fact	Percentiles use percent levels.
CutPointsDivideIntoEqualGroups	Fact	Cut points divide into equal groups.
InterpercentileRangeIsDifferenceOfPercentiles	Fact	Interpercentile range is difference of percentiles.
FiveNumberSummaryProvidesBoxPlotFences	Fact	Five number summary provides box plot fences.
PercentileRankOfValueHandlesTies	Fact	Percentile rank of value handles ties.
PercentileRanksOfValuesKeepPositionsAndMissing	Fact	Percentile ranks of values keep positions and missing.
RanksHandleEveryTieMethod	Fact	Ranks handle every tie method.
ThresholdShareCountsBothSides	Fact	Threshold share counts both sides.
CumulativeSumSkipsMissingButKeepsPositions	Fact	Cumulative sum skips missing but keeps positions.
CumulativeProductCompoundsFactors	Fact	Cumulative product compounds factors.
CumulativeMaximumIsHighWaterMark	Fact	Cumulative maximum is high water mark.
CumulativeMinimumIsLowWaterMark	Fact	Cumulative minimum is low water mark.
RollingStatisticComputesTrailingWindows	Fact	Rolling statistic computes trailing windows.
ExpandingStatisticUsesEverythingSoFar	Fact	Expanding statistic uses everything so far.
ExponentialMovingAverageFollowsRecursion	Fact	Exponential moving average follows recursion.
FrequencyTableOfCategoriesCountsAndAccumulates	Fact	Frequency table of categories counts and accumulates.
FrequencyTableOfIntegersOrdersNumerically	Fact	Frequency table of integers orders numerically.
FrequencyTableOfNumbersFindsRepeatedAmounts	Fact	Frequency table of numbers finds repeated amounts.
RareCategoriesListsSingletons	Fact	Rare categories lists singletons.
VarianceMatchesPopulationAndSampleForms	Fact	Variance matches population and sample forms.
StandardDeviationMatchesWikipediaExample	Fact	Standard deviation matches wikipedia example.
StandardErrorIsSdOverRootN	Fact	Standard error is sd over root n.
CoefficientOfVariationIsSdOverMean	Fact	Coefficient of variation is sd over mean.
VarianceToMeanRatioFlagsOverdispersion	Fact	Variance to mean ratio flags overdispersion.
MeanAbsoluteDeviationAroundMeanAndMedian	Fact	Mean absolute deviation around mean and median.
MedianAbsoluteDeviationIsRobustToOutlier	Fact	Median absolute deviation is robust to outlier.
InterquartileRangeUsesChosenInterpolation	Fact	Interquartile range uses chosen interpolation.
QuartileCoefficientOfDispersionIsQuartileRatio	Fact	Quartile coefficient of dispersion is quartile ratio.
SumOfSquaredDeviationsIsThirtyTwo	Fact	Sum of squared deviations is thirty two.
WeightedVarianceFrequencyAndReliabilityCorrections	Fact	Weighted variance frequency and reliability corrections.
WeightedStandardDeviationIsRootOfWeightedVariance	Fact	Weighted standard deviation is root of weighted variance.
ExponentialWeightedVarianceOfConstantSeriesIsZero	Fact	Exponential weighted variance of constant series is zero.
PooledVarianceWeightsByDegreesOfFreedom	Fact	Pooled variance weights by degrees of freedom.
PooledStandardDeviationIsRootOfPooledVariance	Fact	Pooled standard deviation is root of pooled variance.
PooledVarianceFromSummariesMatchesRawData	Fact	Pooled variance from summaries matches raw data.
SkewnessMatchesMomentCoefficient	Fact	Skewness matches moment coefficient.
ExcessKurtosisMatchesMomentCoefficient	Fact	Excess kurtosis matches moment coefficient.
KurtosisIsExcessPlusThree	Fact	Kurtosis is excess plus three.
ShapeStatisticsCombinesAllThree	Fact	Shape statistics combines all three.
RawMomentsMatchHandComputation	Fact	Raw moments match hand computation.
CentralMomentsMatchHandComputation	Fact	Central moments match hand computation.
StandardisedMomentsRecoverSkewnessAndKurtosis	Fact	Standardised moments recover skewness and kurtosis.
EntropyOfCountsMatchesInformationTheoryExamples	Fact	Entropy of counts matches information theory examples.
EntropyOfCategoriesUsesObservedFrequencies	Fact	Entropy of categories uses observed frequencies.
InequalityMeasuresForOneToFour	Fact	Inequality measures for one to four.
GiniCoefficientOfConsecutiveIntegers	Fact	Gini coefficient of consecutive integers.
GeometricStandardDeviationIsExpOfLogSd	Fact	Geometric standard deviation is exp of log sd.
SummariseColumnsGivesOneRowPerColumn	Fact	Summarise columns gives one row per column.
SummariseColumnsHandlesMissingSingleAndAllMissingColumns	Fact	Summarise columns handles missing single and all missing columns.
DescribeColumnProfilesTextbookExample	Fact	Describe column profiles textbook example.
DescribeColumnHandlesConstantMissingAndNegativeData	Fact	Describe column handles constant missing and negative data.
DescribeTableFindsCorrelationsConstantsSkewAndGaps	Fact	Describe table finds correlations constants skew and gaps.
MissingnessProfileCountsCellsAndRows	Fact	Missingness profile counts cells and rows.
CovarianceMatrixMatchesHandComputation	Fact	Covariance matrix matches hand computation.
CorrelationMatrixIsUnitDiagonalAndSymmetric	Fact	Correlation matrix is unit diagonal and symmetric.
StrongestCorrelationsAreRankedByAbsoluteValue	Fact	Strongest correlations are ranked by absolute value.
SummariseRowsAggregatesAcrossColumns	Fact	Summarise rows aggregates across columns.
SummariseByGroupSplitsStatistics	Fact	Summarise by group splits statistics.
SummariseCategoriesProfilesLabels	Fact	Summarise categories profiles labels.
TopShareConcentrationMatchesHandComputation	Fact	Top share concentration matches hand computation.
ZScoresStandardiseTextbookExample	Fact	Z scores standardise textbook example.
RobustZScoresUseMedianAndMad	Fact	Robust z scores use median and mad.
CentreValuesSubtractsMeanOrMedian	Fact	Centre values subtracts mean or median.
TransformValuesAppliesAndValidatesDomain	Fact	Transform values applies and validates domain.
ProportionsOfTotalSumToOne	Fact	Proportions of total sum to one.
WinsoriseValuesCapsAtPercentiles	Fact	Winsorise values caps at percentiles.
ZScoreOutliersFlagTheExtremeValue	Fact	Z score outliers flag the extreme value.
IqrFenceFlagsValuesBeyondTukeyFences	Fact	Iqr fence flags values beyond tukey fences.
MadOutliersUseModifiedZScore	Fact	Mad outliers use modified z score.
QuantilesByColumnReturnsMatrixOfQuantiles	Fact	Quantiles by column returns matrix of quantiles.

DistributionsAndHistogramsFittingToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DistributionsAndHistogramsFittingToolsTests — 22 tests. Category: Unit.

Test	Kind	Verifies
FitExponentialToOneTwoThreeGivesRateOneHalfAndTheClosedFormLikelihood	Fact	Fit exponential to one two three gives rate one half and the closed form likelihood.
FitNormalRecoversTheSampleMean	Fact	Fit normal recovers the sample mean.
FitDiscreteDistributionsMatchTheirClosedFormEstimators	Fact	Fit discrete distributions match their closed form estimators.
FitContinuousClosedFormEstimatorsMatchHandComputation	Fact	Fit continuous closed form estimators match hand computation.
FitRecoversParametersFromAQuantileGridOfTheSameDistribution	Theory	Fit recovers parameters from a quantile grid of the same distribution.
NumericalFitRecoversParametersFromAQuantileGrid	Theory	Numerical fit recovers parameters from a quantile grid.
FitLaplaceAgreesWithMedianAndMeanAbsoluteDeviationClosedForm	Fact	Fit laplace agrees with median and mean absolute deviation closed form.
FitBinomialHoldsTheNumberOfTrialsFixedAndEstimatesTheProbability	Fact	Fit binomial holds the number of trials fixed and estimates the probability.
FitGeneralizedParetoHoldsTheLocationAtTheSmallestObservation	Fact	Fit generalized pareto holds the location at the smallest observation.
FitDistributionExplainsBadInputs	Fact	Fit distribution explains bad inputs.
FitAndScoreGivesTailProbabilitiesUnderTheFittedDistribution	Fact	Fit and score gives tail probabilities under the fitted distribution.
FitAndScoreRejectsEmptyScoringValues	Fact	Fit and score rejects empty scoring values.
RankPutsTheGeneratingExponentialFirstByAic	Fact	Rank puts the generating exponential first by aic.
RankOfCountDataUsesDiscreteCandidatesAndFindsThePoisson	Fact	Rank of count data uses discrete candidates and finds the poisson.
RankHonoursExplicitCandidatesCriterionAndReportsFailures	Fact	Rank honours explicit candidates criterion and reports failures.
RankByAverageAndByEachStatisticOrdersCandidates	Fact	Rank by average and by each statistic orders candidates.
RankRejectsMixedKindsAndTinySamples	Fact	Rank rejects mixed kinds and tiny samples.
QuantileQuantilePlotOfNormalDataAgainstNormalIsAStraightLine	Fact	Quantile quantile plot of normal data against normal is a straight line.
QuantileQuantilePlotUsesTheRequestedPlottingPositionAndFitsWhenParametersAreOmitted	Fact	Quantile quantile plot uses the requested plotting position and fits when parameters are omitted.
QuantileQuantilePlotThinsLongSamplesEvenlyAndValidatesArguments	Fact	Quantile quantile plot thins long samples evenly and validates arguments.
ProbabilityProbabilityPlotOfMatchingDistributionLiesOnTheDiagonal	Fact	Probability probability plot of matching distribution lies on the diagonal.
ProbabilityProbabilityPlotOfAMismatchedDistributionDeviatesFromTheDiagonal	Fact	Probability probability plot of a mismatched distribution deviates from the diagonal.

DistributionsAndHistogramsHistogramToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DistributionsAndHistogramsHistogramToolsTests — 26 tests. Category: Unit.

Test	Kind	Verifies
FixedBinCountOfOneToTenInFiveBinsHasTwoPerBin	Fact	Fixed bin count of one to ten in five bins has two per bin.
FixedBinCountLastBinIncludesTheMaximumAndScalesAndAccumulates	Fact	Fixed bin count last bin includes the maximum and scales and accumulates.
FixedBinCountHandlesConstantSingleAndInvalidInput	Fact	Fixed bin count handles constant single and invalid input.
FixedBinCountCopesWithHugeMagnitudes	Fact	Fixed bin count copes with huge magnitudes.
FixedBinWidthStartsAtTheMinimumAndCoversTheMaximum	Fact	Fixed bin width starts at the minimum and covers the maximum.
FixedBinWidthRejectsNonPositiveWidthsAndAbsurdBinCounts	Fact	Fixed bin width rejects non positive widths and absurd bin counts.
BinningRulesGiveTheTextbookBinCountForOneToOneHundred	Theory	Binning rules give the textbook bin count for one to one hundred.
BinningRuleFallsBackToSturgesWhenTheSpreadMeasureIsZero	Fact	Binning rule falls back to sturges when the spread measure is zero.
CustomEdgesCountIntoUnequalBinsAndReportOutsideValues	Fact	Custom edges count into unequal bins and report outside values.
CustomEdgesMustBeStrictlyIncreasingAndAtLeastTwo	Fact	Custom edges must be strictly increasing and at least two.
SuggestionsListEveryRuleWithItsBinWidth	Fact	Suggestions list every rule with its bin width.
Histogram2DCountsPairsIntoAGridWithMarginals	Fact	Histogram2 d counts pairs into a grid with marginals.
Histogram2DAcceptsExplicitEdgesAndRejectsMismatchedLengths	Fact	Histogram2 d accepts explicit edges and rejects mismatched lengths.
EmpiricalCdfCountsTheShareAtOrBelowEachPoint	Fact	Empirical cdf counts the share at or below each point.
EmpiricalCdfValidatesInput	Fact	Empirical cdf validates input.
EmpiricalCdfStepsGroupRepeatedValues	Fact	Empirical cdf steps group repeated values.
EmpiricalQuantilesFollowTheStandardDefinitions	Fact	Empirical quantiles follow the standard definitions.
EmpiricalQuantilesValidateProbabilities	Fact	Empirical quantiles validate probabilities.
GaussianKernelDensityMatchesTheHandComputedSumOfBumps	Fact	Gaussian kernel density matches the hand computed sum of bumps.
EpanechnikovAndUniformKernelsHaveFiniteSupport	Fact	Epanechnikov and uniform kernels have finite support.
KernelDensityUsesTheNamedBandwidthRuleAndValidatesInput	Fact	Kernel density uses the named bandwidth rule and validates input.
KernelDensityCurveIntegratesToOneAndFindsASinglePeakForBellShapedData	Fact	Kernel density curve integrates to one and finds a single peak for bell shaped data.
KernelDensityCurveFindsTwoPeaksForBimodalData	Fact	Kernel density curve finds two peaks for bimodal data.
KernelDensityCurveValidatesItsArguments	Fact	Kernel density curve validates its arguments.
BandwidthRulesReportEveryRuleWithItsInputs	Fact	Bandwidth rules report every rule with its inputs.
BandwidthRulesOmitRulesThatCannotBeComputed	Fact	Bandwidth rules omit rules that cannot be computed.

DistributionsAndHistogramsMultivariateToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DistributionsAndHistogramsMultivariateToolsTests — 33 tests. Category: Unit.

Test	Kind	Verifies
StandardBivariateNormalDensityAtTheOriginIsOneOverTwoPi	Fact	Standard bivariate normal density at the origin is one over two pi.
CorrelatedNormalDensityUsesTheInverseCovariance	Fact	Correlated normal density uses the inverse covariance.
NormalDensityValidatesShapeSymmetryAndDefiniteness	Fact	Normal density validates shape symmetry and definiteness.
MahalanobisDistanceAndChiSquareTailFollowTheClosedForms	Fact	Mahalanobis distance and chi square tail follow the closed forms.
OutlierScoresRankAnObviousOutlierFirst	Fact	Outlier scores rank an obvious outlier first.
OutlierScoresSumOfSquaredDistancesEqualsNMinusOneTimesPForTheSample	Fact	Outlier scores sum of squared distances equals n minus one times p for the sample.
OutlierScoresRejectSingularOrTooSmallSamples	Fact	Outlier scores reject singular or too small samples.
FitMatchesHandComputedMeanCovarianceCorrelationAndLikelihood	Fact	Fit matches hand computed mean covariance correlation and likelihood.
FitRejectsTooFewRowsAndMissingValues	Fact	Fit rejects too few rows and missing values.
NormalSampleIsReproducibleWithTheRightMeanAndCovariance	Fact	Normal sample is reproducible with the right mean and covariance.
OrthantProbabilitiesMatchClosedFormsInOneAndTwoDimensions	Fact	Orthant probabilities match closed forms in one and two dimensions.
OrthantProbabilityLimitsDimensionality	Fact	Orthant probability limits dimensionality.
DirichletSummaryMatchesTheClosedFormMomentsAndCovariance	Fact	Dirichlet summary matches the closed form moments and covariance.
DirichletDensityAtTheMeanMatchesTheHandComputedValue	Fact	Dirichlet density at the mean matches the hand computed value.
DirichletDensityRejectsPointsOffTheSimplex	Fact	Dirichlet density rejects points off the simplex.
DirichletSampleRowsSumToOneAndAverageToTheMean	Fact	Dirichlet sample rows sum to one and average to the mean.
DirichletFitRecoversTheConcentrationsOfALargeSample	Fact	Dirichlet fit recovers the concentrations of a large sample.
DirichletFitRejectsRowsThatAreNotProportions	Fact	Dirichlet fit rejects rows that are not proportions.
MultinomialSummaryMatchesTheClosedForms	Fact	Multinomial summary matches the closed forms.
MultinomialProbabilityMatchesTheFactorialFormula	Fact	Multinomial probability matches the factorial formula.
MultinomialSampleRowsSumToTheTrialsAndAverageToTheMean	Fact	Multinomial sample rows sum to the trials and average to the mean.
WishartSummaryMatchesTheClosedFormMeanAndVariance	Fact	Wishart summary matches the closed form mean and variance.
WishartRejectsTooFewDegreesAndBadScale	Fact	Wishart rejects too few degrees and bad scale.
OneByOneWishartIsAChiSquare	Fact	One by one wishart is a chi square.
WishartDensityIsZeroForAMatrixThatIsNotPositiveDefinite	Fact	Wishart density is zero for a matrix that is not positive definite.
WishartSamplesAreSymmetricPositiveDefiniteAndAverageToDegreesTimesScale	Fact	Wishart samples are symmetric positive definite and average to degrees times scale.
InverseWishartSummaryMatchesTheOneByOneClosedForms	Fact	Inverse wishart summary matches the one by one closed forms.
InverseWishartDensityMatchesTheOneByOneClosedForm	Fact	Inverse wishart density matches the one by one closed form.
CircularVonMisesFisherDensityMatchesTheBesselClosedForm	Fact	Circular von mises fisher density matches the bessel closed form.
VonMisesFisherDensityRejectsOddDimensionsAndZeroDirections	Fact	Von mises fisher density rejects odd dimensions and zero directions.
SphericalVonMisesFisherSamplesAreUnitVectorsWithTheMeanResultantLength	Fact	Spherical von mises fisher samples are unit vectors with the mean resultant length.
SphereSamplesLieOnTheSurfaceAndAverageToTheCentre	Fact	Sphere samples lie on the surface and average to the centre.
BallSamplesLieInsideAndHaveTwoThirdsMeanRadiusInTwoDimensions	Fact	Ball samples lie inside and have two thirds mean radius in two dimensions.

DistributionsAndHistogramsShapeTailAndMixtureToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DistributionsAndHistogramsShapeTailAndMixtureToolsTests — 19 tests. Category: Unit.

Test	Kind	Verifies
ShapeSummaryMatchesTheHandComputedSkewnessKurtosisAndJarqueBera	Fact	Shape summary matches the hand computed skewness kurtosis and jarque bera.
ShapeSummaryFlagsSkewAndTailWeight	Fact	Shape summary flags skew and tail weight.
ShapeSummaryRejectsConstantTinyAndMissingData	Fact	Shape summary rejects constant tiny and missing data.
QuantileExceedanceMatchesHandComputationForOneToOneHundred	Fact	Quantile exceedance matches hand computation for one to one hundred.
QuantileExceedanceLowerTailAndValidation	Fact	Quantile exceedance lower tail and validation.
ThresholdExceedanceReportsCountsAndMeanExcess	Fact	Threshold exceedance reports counts and mean excess.
ThresholdExceedanceValidatesInput	Fact	Threshold exceedance validates input.
ExponentialTailGivesShapeNearZeroAndTheClosedFormReturnLevel	Fact	Exponential tail gives shape near zero and the closed form return level.
HeavyTailGivesPositiveShape	Fact	Heavy tail gives positive shape.
GeneralizedParetoTailValidatesItsArguments	Fact	Generalized pareto tail validates its arguments.
TwoSeparatedClustersAreRecoveredAsTwoComponents	Fact	Two separated clusters are recovered as two components.
SingleComponentEqualsTheNormalMaximumLikelihoodAndResponsibilitiesAreOptional	Fact	Single component equals the normal maximum likelihood and responsibilities are optional.
MixtureFitIsReproducibleForASeedAndValidatesInput	Fact	Mixture fit is reproducible for a seed and validates input.
ComponentSelectionPicksTwoForTwoSeparatedClusters	Fact	Component selection picks two for two separated clusters.
ComponentSelectionStopsWhenValuesRunOut	Fact	Component selection stops when values run out.
LognormalMixtureRecoversTwoLogScaleGroups	Fact	Lognormal mixture recovers two log scale groups.
MixtureModelRejectsUnsupportedFamiliesAndBadData	Fact	Mixture model rejects unsupported families and bad data.
MixtureEvaluationMatchesTheHandComputedDensityCumulativeAndResponsibilities	Fact	Mixture evaluation matches the hand computed density cumulative and responsibilities.
MixtureEvaluationValidatesWeightsAndParameters	Fact	Mixture evaluation validates weights and parameters.

DistributionsAndHistogramsUnivariateToolsTests

Jube.Test.AdvancedAnalytics.Statistics.DistributionsAndHistogramsUnivariateToolsTests — 33 tests. Category: Unit.

Test	Kind	Verifies
ListDistributionsDescribesEveryKindWithParameterNamesAndFitSupport	Fact	List distributions describes every kind with parameter names and fit support.
EveryListedDistributionAcceptsItsOwnExampleParametersInDescribe	Fact	Every listed distribution accepts its own example parameters in describe.
DescribeNormalMatchesClosedFormMoments	Fact	Describe normal matches closed form moments.
DescribeMatchesTextbookMeanAndVariance	Theory	Describe matches textbook mean and variance.
DescribeUniformDiscreteEntropyIsLogOfTheNumberOfOutcomes	Fact	Describe uniform discrete entropy is log of the number of outcomes.
DescribeReportsNullForMomentsThatDoNotExist	Fact	Describe reports null for moments that do not exist.
DescribeRejectsWrongParameterCountAndDomains	Fact	Describe rejects wrong parameter count and domains.
DensityOfStandardNormalAtZeroIsOneOverRootTwoPi	Fact	Density of standard normal at zero is one over root two pi.
DensityMatchesClosedForms	Theory	Density matches closed forms.
DiscreteDensityIsExactProbabilityMassAndZeroBetweenIntegers	Fact	Discrete density is exact probability mass and zero between integers.
DensityValidatesInputs	Fact	Density validates inputs.
LogDensityIsNaturalLogAndSurvivesTheFarTail	Fact	Log density is natural log and survives the far tail.
CumulativeProbabilityMatchesTablesAndLimits	Fact	Cumulative probability matches tables and limits.
DiscreteCumulativeProbabilityRoundsDownToWholeNumbers	Fact	Discrete cumulative probability rounds down to whole numbers.
UpperTailProbabilityIsAccurateInTheFarTail	Fact	Upper tail probability is accurate in the far tail.
QuantileMatchesPublishedCriticalValues	Fact	Quantile matches published critical values.
QuantileOfDiscreteIsSmallestWholeNumberReachingTheProbability	Fact	Quantile of discrete is smallest whole number reaching the probability.
QuantileRejectsProbabilitiesOutsideZeroOne	Fact	Quantile rejects probabilities outside zero one.
HazardRateIsConstantForExponentialAndRisingForWeibullAboveOne	Fact	Hazard rate is constant for exponential and rising for weibull above one.
CumulativeHazardIsMinusLogOfTheUpperTail	Fact	Cumulative hazard is minus log of the upper tail.
IntervalProbabilityIsDifferenceOfCumulativeProbabilities	Fact	Interval probability is difference of cumulative probabilities.
IntervalProbabilityRejectsMismatchedOrReversedEnds	Fact	Interval probability rejects mismatched or reversed ends.
CurveSpansTheRequestedQuantilesAndCumulativeIsMonotone	Fact	Curve spans the requested quantiles and cumulative is monotone.
CurveValidatesItsArguments	Fact	Curve validates its arguments.
ProbabilityTableListsExactMassesAndTotals	Fact	Probability table lists exact masses and totals.
ProbabilityTableRejectsContinuousDistributionsAndBadRanges	Fact	Probability table rejects continuous distributions and bad ranges.
RandomSampleIsReproducibleAndHasTheRightMoments	Fact	Random sample is reproducible and has the right moments.
RandomSampleOfDiscreteDistributionsGivesWholeNumbersInSupport	Fact	Random sample of discrete distributions gives whole numbers in support.
RandomSampleValidatesCountAndSupport	Fact	Random sample validates count and support.
LogLikelihoodSumsLogDensitiesAndComputesAicAndBic	Fact	Log likelihood sums log densities and computes aic and bic.
LogLikelihoodIsNullWhenAnObservationIsImpossible	Fact	Log likelihood is null when an observation is impossible.
TailScoresGiveLowerUpperTwoSidedAndSurprise	Fact	Tail scores give lower upper two sided and surprise.
TailScoresOfDiscreteValuesIncludeTheValueInBothTails	Fact	Tail scores of discrete values include the value in both tails.

HypothesisTestsToolsTests

Jube.Test.AdvancedAnalytics.Statistics.HypothesisTestsToolsTests — 143 tests.

Test	Kind	Verifies
ChiSquareGoodnessOfFitTestMatchesMendelsPeaData	Fact	Chi square goodness of fit test matches mendels pea data.
ChiSquareGoodnessOfFitTestDefaultsToAnEvenSplitAndReducesDegreesOfFreedom	Fact	Chi square goodness of fit test defaults to an even split and reduces degrees of freedom.
ChiSquareGoodnessOfFitTestWarnsForSparseCategoriesAndRejectsBadInput	Fact	Chi square goodness of fit test warns for sparse categories and rejects bad input.
ChiSquareIndependenceTestTwoByTwoMatchesClosedForm	Fact	Chi square independence test two by two matches closed form.
ChiSquareIndependenceTestTwoByThreeUsesRowsMinusOneTimesColumnsMinusOneDegrees	Fact	Chi square independence test two by three uses rows minus one times columns minus one degrees.
ChiSquareIndependenceTestRejectsBadTablesAndWarnsForSmallExpectedCounts	Fact	Chi square independence test rejects bad tables and warns for small expected counts.
FisherExactTestMatchesFishersLadyTastingTea	Fact	Fisher exact test matches fishers lady tasting tea.
FisherExactTestHandlesZeroCellsAndRejectsNonTwoByTwo	Fact	Fisher exact test handles zero cells and rejects non two by two.
McNemarTestMatchesTheWikipediaWorkedExample	Fact	Mc nemar test matches the wikipedia worked example.
McNemarTestRejectsNoDiscordantPairsAndWarnsForFewOfThem	Fact	Mc nemar test rejects no discordant pairs and warns for few of them.
BowkerSymmetryTestMatchesHandComputation	Fact	Bowker symmetry test matches hand computation.
BowkerSymmetryTestRejectsAnEmptySymmetricPairAndNonSquareTables	Fact	Bowker symmetry test rejects an empty symmetric pair and non square tables.
StuartMaxwellHomogeneityTestMatchesHandComputation	Fact	Stuart maxwell homogeneity test matches hand computation.
BhapkarHomogeneityTestMatchesHandComputation	Fact	Bhapkar homogeneity test matches hand computation.
CohensKappaTestMatchesTheGrantProposalExample	Fact	Cohens kappa test matches the grant proposal example.
CohensKappaTestAgainstANonZeroHypothesisUsesTheGeneralStandardError	Fact	Cohens kappa test against a non zero hypothesis uses the general standard error.
CohensKappaTestRejectsBadInput	Fact	Cohens kappa test rejects bad input.
WeightedKappaTestMatchesHandComputationForBothWeightings	Fact	Weighted kappa test matches hand computation for both weightings.
WeightedKappaTestRejectsBadInput	Fact	Weighted kappa test rejects bad input.
KappaComparisonTestMatchesHandComputation	Fact	Kappa comparison test matches hand computation.
KappaHomogeneityTestMatchesInverseVarianceComputation	Fact	Kappa homogeneity test matches inverse variance computation.
KappaGroupDifferenceTestComparesTheMeanKappasOfTwoGroups	Fact	Kappa group difference test compares the mean kappas of two groups.
AucSignificanceTestMatchesDeLongHandComputation	Fact	Auc significance test matches de long hand computation.
AucSignificanceTestReportsAnInvertedScoreBelowHalf	Fact	Auc significance test reports an inverted score below half.
AucSignificanceTestRejectsBadInput	Fact	Auc significance test rejects bad input.
AucComparisonTestMatchesDeLongCovarianceHandComputation	Fact	Auc comparison test matches de long covariance hand computation.
AucComparisonTestRejectsIdenticalModelsAndBadInput	Fact	Auc comparison test rejects identical models and bad input.
OneSampleTTestMatchesPublishedSleepGroupTwoResult	Fact	One sample t test matches published sleep group two result.
OneSampleTTestOneSidedTailsSplitTheTwoSidedPValue	Fact	One sample t test one sided tails split the two sided p value.
OneSampleTTestOneSidedIntervalIsStillTheTwoSidedIntervalAtOneMinusAlpha	Fact	One sample t test one sided interval is still the two sided interval at one minus alpha.
OneSampleTTestNonRejectionUsesAlpha	Fact	One sample t test non rejection uses alpha.
OneSampleTTestWhenMeanEqualsHypothesisGivesZeroStatisticAndPValueOne	Fact	One sample t test when mean equals hypothesis gives zero statistic and p value one.
OneSampleTTestRejectsBadInputWithTheParameterName	Fact	One sample t test rejects bad input with the parameter name.
OneSampleTTestHandlesHugeMagnitudesWithoutLosingTheStatistic	Fact	One sample t test handles huge magnitudes without losing the statistic.
OneSampleTTestFromSummaryEqualsTheRawResult	Fact	One sample t test from summary equals the raw result.
OneSampleTTestFromSummaryRejectsNonPositiveSpreadAndTinySamples	Fact	One sample t test from summary rejects non positive spread and tiny samples.
TwoSampleTTestWelchMatchesPublishedSleepResult	Fact	Two sample t test welch matches published sleep result.
TwoSampleTTestPooledMatchesPublishedSleepResult	Fact	Two sample t test pooled matches published sleep result.
TwoSampleTTestOneSidedDirectionIsGroupOneMinusGroupTwo	Fact	Two sample t test one sided direction is group one minus group two.
TwoSampleTTestWarnsWhenPooledButVariancesAreVeryDifferent	Fact	Two sample t test warns when pooled but variances are very different.
TwoSampleTTestRejectsBadInput	Fact	Two sample t test rejects bad input.
TwoSampleTTestFromSummaryEqualsTheRawWelchResult	Fact	Two sample t test from summary equals the raw welch result.
TwoSampleTTestFromSummaryRejectsBadInput	Fact	Two sample t test from summary rejects bad input.
PairedTTestMatchesPublishedSleepResult	Fact	Paired t test matches published sleep result.
PairedTTestRejectsMismatchedLengthsAndIdenticalPairs	Fact	Paired t test rejects mismatched lengths and identical pairs.
OneSampleZTestWithKnownSigmaMatchesClosedForm	Fact	One sample z test with known sigma matches closed form.
OneSampleZTestWithSampleSpreadWarnsForSmallSamples	Fact	One sample z test with sample spread warns for small samples.
OneSampleZTestRejectsBadSigmaAndConstantSampleWithoutSigma	Fact	One sample z test rejects bad sigma and constant sample without sigma.
TwoSampleZTestMatchesClosedForm	Fact	Two sample z test matches closed form.
TwoSampleZTestRejectsBadInputAndWarnsForSmallGroups	Fact	Two sample z test rejects bad input and warns for small groups.
TwoSampleZTestFromSummaryEqualsRawResult	Fact	Two sample z test from summary equals raw result.
WaldZTestMatchesClosedForm	Fact	Wald z test matches closed form.
OneProportionZTestSixtyHeadsInAHundredTossesGivesZTwo	Fact	One proportion z test sixty heads in a hundred tosses gives z two.
OneProportionZTestWarnsForSparseExpectedCountsAndRejectsBadInput	Fact	One proportion z test warns for sparse expected counts and rejects bad input.
TwoProportionZTestMatchesPooledClosedForm	Fact	Two proportion z test matches pooled closed form.
TwoProportionZTestRejectsDegenerateAndBadInput	Fact	Two proportion z test rejects degenerate and bad input.
BinomialExactTestMatchesPublishedSixtyOfHundredResult	Fact	Binomial exact test matches published sixty of hundred result.
BinomialExactTestHandlesBoundariesAndBadInput	Fact	Binomial exact test handles boundaries and bad input.
BinomialExactTestFromOutcomesCountsTheTrueValues	Fact	Binomial exact test from outcomes counts the true values.
FTestTwoVariancesMatchesClosedFormOnPlantGrowth	Fact	F test two variances matches closed form on plant growth.
FTestTwoVariancesRejectsBadInput	Fact	F test two variances rejects bad input.
FTestTwoVariancesFromSummaryEqualsRawResult	Fact	F test two variances from summary equals raw result.
LeveneTestBrownForsytheMatchesPublishedPlantGrowthResult	Fact	Levene test brown forsythe matches published plant growth result.
LeveneTestMeanCentreMatchesClosedForm	Fact	Levene test mean centre matches closed form.
LeveneTestTrimmedMeanRunsAndRejectsBadInput	Fact	Levene test trimmed mean runs and rejects bad input.
BartlettTestMatchesPublishedPlantGrowthResult	Fact	Bartlett test matches published plant growth result.
BartlettTestRejectsConstantGroupAndSingleGroup	Fact	Bartlett test rejects constant group and single group.
OneWayAnovaMatchesPublishedPlantGrowthTable	Fact	One way anova matches published plant growth table.
OneWayAnovaWithPerfectlySeparatedConstantGroupsHasInfiniteF	Fact	One way anova with perfectly separated constant groups has infinite f.
OneWayAnovaFromLabelsEqualsTheGroupedResult	Fact	One way anova from labels equals the grouped result.
TwoWayAnovaFixedEffectsTestsEverythingAgainstErrorMeanSquare	Fact	Two way anova fixed effects tests everything against error mean square.
TwoWayAnovaRandomEffectsTestsFactorsAgainstTheInteraction	Fact	Two way anova random effects tests factors against the interaction.
TwoWayAnovaMixedModelTestsFactorAAgainstInteractionAndFactorBAgainstError	Fact	Two way anova mixed model tests factor a against interaction and factor b against error.
TwoWayAnovaRejectsUnbalancedAndMalformedDesigns	Fact	Two way anova rejects unbalanced and malformed designs.
GrubbsOutlierTestFlagsTheGrossOutlier	Fact	Grubbs outlier test flags the gross outlier.
GrubbsOutlierTestRejectsBadInput	Fact	Grubbs outlier test rejects bad input.
EffectSizeTwoSamplesMatchesClosedFormOnSleepData	Fact	Effect size two samples matches closed form on sleep data.
EffectSizeTwoSamplesRejectsBadInput	Fact	Effect size two samples rejects bad input.
EffectSizeFromSummaryMatchesRawResult	Fact	Effect size from summary matches raw result.
OneSampleTTestPowerAnalysisSolvesPowerForHalfSdEffectAndThirtyFourObservations	Fact	One sample t test power analysis solves power for half sd effect and thirty four observations.
OneSampleTTestPowerAnalysisNeedsThirtyFourObservationsForPowerEightyAtHalfSd	Fact	One sample t test power analysis needs thirty four observations for power eighty at half sd.
OneSampleTTestPowerAnalysisSolvesTheDetectableEffect	Fact	One sample t test power analysis solves the detectable effect.
OneSampleTTestPowerAnalysisRejectsMissingOrInvalidInputs	Fact	One sample t test power analysis rejects missing or invalid inputs.
OneSampleZTestPowerAnalysisMatchesTheClosedForm	Fact	One sample z test power analysis matches the closed form.
OneSampleZTestPowerAnalysisLessTailMirrorsTheGreaterTail	Fact	One sample z test power analysis less tail mirrors the greater tail.
OneSampleZTestPowerAnalysisRoundTripsTheEffectSize	Fact	One sample z test power analysis round trips the effect size.
TwoSampleTTestPowerAnalysisNeedsSixtyFourPerGroupForHalfSdAtPowerEighty	Fact	Two sample t test power analysis needs sixty four per group for half sd at power eighty.
TwoSampleTTestPowerAnalysisSupportsUnequalAllocationAndRejectsBadInput	Fact	Two sample t test power analysis supports unequal allocation and rejects bad input.
TwoSampleZTestPowerAnalysisNeedsSixtyThreePerGroupForHalfSdAtPowerEighty	Fact	Two sample z test power analysis needs sixty three per group for half sd at power eighty.
TwoSampleZTestPowerAnalysisSolvesEffectAndRejectsBadInput	Fact	Two sample z test power analysis solves effect and rejects bad input.
MeanConfidenceIntervalMatchesPublishedSleepGroupIntervals	Fact	Mean confidence interval matches published sleep group intervals.
MeanConfidenceIntervalWidensWithConfidenceAndRejectsBadInput	Fact	Mean confidence interval widens with confidence and rejects bad input.
ProportionConfidenceIntervalMatchesClosedFormsForSixtyOfHundred	Fact	Proportion confidence interval matches closed forms for sixty of hundred.
ProportionConfidenceIntervalIsClippedAtTheBoundsAndWarnsForWaldWithFewSuccesses	Fact	Proportion confidence interval is clipped at the bounds and warns for wald with few successes.
VarianceConfidenceIntervalMatchesChiSquareHandComputation	Fact	Variance confidence interval matches chi square hand computation.
VarianceConfidenceIntervalRejectsBadInput	Fact	Variance confidence interval rejects bad input.
MedianConfidenceIntervalForElevenValuesIsTheSecondToTenthOrderStatistic	Fact	Median confidence interval for eleven values is the second to tenth order statistic.
MedianConfidenceIntervalReturnsTheRangeWithAWarningWhenTheSampleIsTooSmall	Fact	Median confidence interval returns the range with a warning when the sample is too small.
AdjustPValuesBonferroniMultipliesByTheNumberOfTests	Fact	Adjust p values bonferroni multiplies by the number of tests.
AdjustPValuesHolmIsStepDownAndMonotone	Fact	Adjust p values holm is step down and monotone.
AdjustPValuesBenjaminiHochbergControlsTheFalseDiscoveryRate	Fact	Adjust p values benjamini hochberg controls the false discovery rate.
AdjustPValuesByMethodCoversSidakHochbergAndBenjaminiYekutieli	Fact	Adjust p values by method covers sidak hochberg and benjamini yekutieli.
AdjustPValuesRejectsEmptyOutOfRangeAndNaNAndKeepsASingleValueUnchanged	Fact	Adjust p values rejects empty out of range and na n and keeps a single value unchanged.
PValueFromTestStatisticMatchesClosedFormsForEachDistribution	Fact	P value from test statistic matches closed forms for each distribution.
PValueFromTestStatisticSupportsLowerTailAndRejectsMissingDegrees	Fact	P value from test statistic supports lower tail and rejects missing degrees.
CriticalValueForSignificanceLevelMatchesTextbookValues	Fact	Critical value for significance level matches textbook values.
CriticalValueForSignificanceLevelOneSidedLowerTailAndBadInput	Fact	Critical value for significance level one sided lower tail and bad input.
RecommendHypothesisTestChoosesTheClassicTestForEachCommonSituation	Fact	Recommend hypothesis test chooses the classic test for each common situation.
RecommendHypothesisTestOnlyNamesToolsThatExist	Fact	Recommend hypothesis test only names tools that exist.
RecommendHypothesisTestRejectsBadCounts	Fact	Recommend hypothesis test rejects bad counts.
EveryHypothesisToolIsSelfDescribedWithoutTheLibraryName	Fact	Every hypothesis tool is self described without the library name.
MannWhitneyUTestCompleteSeparationHasExactPValueOneTenth	Fact	Mann whitney u test complete separation has exact p value one tenth.
MannWhitneyUTestMatchesPublishedHollanderWolfeExample	Fact	Mann whitney u test matches published hollander wolfe example.
MannWhitneyUTestWithTiesUsesApproximationAndWarns	Fact	Mann whitney u test with ties uses approximation and warns.
MannWhitneyUTestRejectsBadInput	Fact	Mann whitney u test rejects bad input.
WilcoxonSignedRankTestOfDifferencesMatchesPublishedDepressionExample	Fact	Wilcoxon signed rank test of differences matches published depression example.
WilcoxonSignedRankTestDropsZerosAndRejectsAllZeroInput	Fact	Wilcoxon signed rank test drops zeros and rejects all zero input.
WilcoxonSignedRankPairedTestMatchesPublishedDepressionExample	Fact	Wilcoxon signed rank paired test matches published depression example.
WilcoxonSignedRankPairedTestRejectsMismatchAndIdenticalPairs	Fact	Wilcoxon signed rank paired test rejects mismatch and identical pairs.
SignTestOneSampleCountsFivePositivesOfNineteenAndSaysMedianIsBelow	Fact	Sign test one sample counts five positives of nineteen and says median is below.
SignTestOneSampleRejectsAllTiedAndEmptyInput	Fact	Sign test one sample rejects all tied and empty input.
SignTestPairedAgreesWithTheOneSampleTestOnTheSameSigns	Fact	Sign test paired agrees with the one sample test on the same signs.
SignTestPairedRejectsMismatchAndAllTied	Fact	Sign test paired rejects mismatch and all tied.
SignTestFromCountsUsesTheExactBinomial	Fact	Sign test from counts uses the exact binomial.
KolmogorovSmirnovOneSampleTestUniformExampleHasStatisticPointOneFive	Fact	Kolmogorov smirnov one sample test uniform example has statistic point one five.
KolmogorovSmirnovOneSampleTestRejectsAWronglyCentredNormal	Fact	Kolmogorov smirnov one sample test rejects a wrongly centred normal.
KolmogorovSmirnovOneSampleTestSupportsExponentialAndLogNormalAndRejectsBadParameters	Fact	Kolmogorov smirnov one sample test supports exponential and log normal and rejects bad parameters.
KolmogorovSmirnovTwoSampleTestHandComputedStatisticIsHalf	Fact	Kolmogorov smirnov two sample test hand computed statistic is half.
KolmogorovSmirnovTwoSampleTestDetectsDisjointSamplesAndRejectsEmpty	Fact	Kolmogorov smirnov two sample test detects disjoint samples and rejects empty.
ShapiroWilkNormalityTestMatchesThePaperExampleWithinApproximationError	Fact	Shapiro wilk normality test matches the paper example within approximation error.
ShapiroWilkNormalityTestAcceptsNormalQuantilesAndRejectsBadInput	Fact	Shapiro wilk normality test accepts normal quantiles and rejects bad input.
AndersonDarlingNormalityTestMatchesHandComputedStatistic	Fact	Anderson darling normality test matches hand computed statistic.
AndersonDarlingNormalityTestAcceptsNormalQuantilesAndRejectsBadInput	Fact	Anderson darling normality test accepts normal quantiles and rejects bad input.
LillieforsNormalityTestRejectsSkewedDataAndAcceptsNormalQuantiles	Fact	Lilliefors normality test rejects skewed data and accepts normal quantiles.
LillieforsNormalityTestRejectsBadInput	Fact	Lilliefors normality test rejects bad input.
JarqueBeraNormalityTestMatchesClosedForm	Fact	Jarque bera normality test matches closed form.
JarqueBeraNormalityTestRejectsBadInput	Fact	Jarque bera normality test rejects bad input.
ChiSquareDistributionFitTestAcceptsEvenlySpreadUniformData	Fact	Chi square distribution fit test accepts evenly spread uniform data.
ChiSquareDistributionFitTestRejectsWrongReferenceAndBadInput	Fact	Chi square distribution fit test rejects wrong reference and bad input.
KruskalWallisTestMatchesPublishedHollanderWolfeExample	Fact	Kruskal wallis test matches published hollander wolfe example.
KruskalWallisTestAppliesTheTieCorrection	Fact	Kruskal wallis test applies the tie correction.
KruskalWallisTestRejectsBadInput	Fact	Kruskal wallis test rejects bad input.
EveryHypothesisToolFailsOnlyWithArgumentExceptionsWhateverTheInput	Fact	Every hypothesis tool fails only with argument exceptions whatever the input.

ModelEvaluationMulticlassAndAnomalyTests

Jube.Test.AdvancedAnalytics.Statistics.ModelEvaluationMulticlassAndAnomalyTests — 3 tests.

Test	Kind	Verifies
MulticlassAlgorithmsRecoverBandedClasses	Fact	Multiclass algorithms recover banded classes.
EveryDetectorScoresKnownOutliersHigher	Fact	Every detector scores known outliers higher.
ContaminationIsEstimatedFromASeparatedGroup	Fact	Contamination is estimated from a separated group.

ModelEvaluationRegressionTests

Jube.Test.AdvancedAnalytics.Statistics.ModelEvaluationRegressionTests — 8 tests.

Test	Kind	Verifies
LinearRegressionRecoversTwoXPlusOneExactly	Fact	Linear regression recovers two x plus one exactly.
RidgeHandlesCollinearPredictorsAndConstantTargetsAreRejected	Fact	Ridge handles collinear predictors and constant targets are rejected.
TreeRegressionLearnsAStepFunction	Fact	Tree regression learns a step function.
NeighbourAndKernelRegressionFitASmoothCurve	Fact	Neighbour and kernel regression fit a smooth curve.
NeuralRegressionIsSeededAndFitsALine	Fact	Neural regression is seeded and fits a line.
RegressorComparisonRanksLinearFirstOnLinearData	Fact	Regressor comparison ranks linear first on linear data.
RegressionImportanceFindsTheSignalVariable	Fact	Regression importance finds the signal variable.
RegressionPartialDependenceIsIncreasingForALine	Fact	Regression partial dependence is increasing for a line.

ModelEvaluationSelectionTests

Jube.Test.AdvancedAnalytics.Statistics.ModelEvaluationSelectionTests — 9 tests.

Test	Kind	Verifies
GridSearchPrefersDepthTwoForAnInteractionAndReportsNestedScoreAsync	Fact	Grid search prefers depth two for an interaction and reports nested score.
RandomSearchIsSeededAndBoundedAsync	Fact	Random search is seeded and bounded.
LearningCurveGrowsTheTrainingRowsAsync	Fact	Learning curve grows the training rows.
ValidationCurveShowsDepthOneUnderfitsAnInteractionAsync	Fact	Validation curve shows depth one underfits an interaction.
PermutationImportanceFlagsTheNoiseVariableAsync	Fact	Permutation importance flags the noise variable.
PartialDependenceIsIncreasingForTheSignalAndFlatForNoiseAsync	Fact	Partial dependence is increasing for the signal and flat for noise.
CalibrationComparisonListsFourMethodsAndPlattBeatsRawNaiveBayes	Fact	Calibration comparison lists four methods and platt beats raw naive bayes.
ScoreCalibrationCorrectsOverconfidentScores	Fact	Score calibration corrects overconfident scores.
ModelComparisonUsesIdenticalFoldsAndRecommendsAnEquivalentModelAsync	Fact	Model comparison uses identical folds and recommends an equivalent model.

ModelEvaluationToolsTests

Jube.Test.AdvancedAnalytics.Statistics.ModelEvaluationToolsTests — 13 tests.

Test	Kind	Verifies
DecisionTreeRecoversTheKnownInteractionForEveryAlgorithm	Fact	Decision tree recovers the known interaction for every algorithm.
DecisionTreeIsDeterministicAndPruningNeverGrowsIt	Fact	Decision tree is deterministic and pruning never grows it.
ClassificationToolsRejectBadInput	Fact	Classification tools reject bad input.
SmallSamplesAndLeakedPredictorsAreWarnedAbout	Fact	Small samples and leaked predictors are warned about.
SevereImbalanceWarnsUnlessHandled	Fact	Severe imbalance warns unless handled.
RandomForestAndBaggingAreAccurateAndDeterministic	Fact	Random forest and bagging are accurate and deterministic.
BothBoostingAlgorithmsSeparateTheClasses	Fact	Both boosting algorithms separate the classes.
NaiveBayesKindsRankTheClasses	Fact	Naive bayes kinds rank the classes.
NearestNeighboursReportTheKSweepWithOneSelection	Fact	Nearest neighbours report the k sweep with one selection.
SupportVectorMachinesSweepComplexity	Fact	Support vector machines sweep complexity.
NeuralNetworkClassifierIsSeededAndAccurate	Fact	Neural network classifier is seeded and accurate.
LogisticCrossValidationPoolsEveryRowOnce	Fact	Logistic cross validation pools every row once.
TestRowsNeverInfluenceTheFitAndValidationRowsOnlyTheCalibration	Fact	Test rows never influence the fit and validation rows only the calibration.

ModelSelectionToolsCachePointerTests

Jube.Test.AdvancedAnalytics.Statistics.ModelSelectionToolsCachePointerTests — 6 tests.

Test	Kind	Verifies
PutModelComparisonDataWithNoBoundWriterIsRefusedAsync	Fact	Put model comparison data with no bound writer is refused.
PutModelComparisonDataDelegatesToTheBoundWriterAndReturnsItsResultAsync	Fact	Put model comparison data delegates to the bound writer and returns its result.
GivingBothInlineRowsAndACachePointerIsRefusedAsync	Fact	Giving both inline rows and a cache pointer is refused.
GivingNeitherInlineRowsNorACachePointerIsRefusedAsync	Fact	Giving neither inline rows nor a cache pointer is refused.
ACachePointerWithNoBoundReaderIsRefusedAsync	Fact	A cache pointer with no bound reader is refused.
ACachePointerResolvesToTheSameResultAsTheIdenticalInlineRowsAsync	Fact	A cache pointer resolves to the same result as the identical inline rows.

MultivariateAndClusteringToolsTests

Jube.Test.AdvancedAnalytics.Statistics.MultivariateAndClusteringToolsTests — 119 tests.

Test	Kind	Verifies
VectorDistanceMatchesClosedFormsForContinuousMetrics	Fact	Vector distance matches closed forms for continuous metrics.
VectorDistanceAngularIsTheArcCosineOfTheCosineSimilarity	Fact	Vector distance angular is the arc cosine of the cosine similarity.
VectorDistanceHellingerFollowsTheStandardDefinition	Fact	Vector distance hellinger follows the standard definition.
VectorDistanceBinaryMetricsMatchHandCounts	Fact	Vector distance binary metrics match hand counts.
VectorDistanceWeightedEuclideanUsesTheWeights	Fact	Vector distance weighted euclidean uses the weights.
VectorDistanceRejectsBadInputWithAnExplanation	Fact	Vector distance rejects bad input with an explanation.
DistanceMatrixWithinSetIsSymmetricWithZeroDiagonal	Fact	Distance matrix within set is symmetric with zero diagonal.
DistanceMatrixWithinSetHandlesSingleRowAndRejectsRaggedAndHugeInput	Fact	Distance matrix within set handles single row and rejects ragged and huge input.
DistanceMatrixBetweenSetsIsRectangular	Fact	Distance matrix between sets is rectangular.
DistanceMatrixBetweenSetsRejectsColumnMismatchAndEmpty	Fact	Distance matrix between sets rejects column mismatch and empty.
KernelValueMatchesClosedForms	Fact	Kernel value matches closed forms.
KernelValueSelfSimilarityOfRadialKernelsIsOneAndBadParametersAreRejected	Fact	Kernel value self similarity of radial kernels is one and bad parameters are rejected.
KernelValueEveryKernelKindEvaluatesFinitelyOnPositiveData	Fact	Kernel value every kernel kind evaluates finitely on positive data.
KernelValueDirichletHandlesEqualCoordinatesByTheirLimit	Fact	Kernel value dirichlet handles equal coordinates by their limit.
KernelGramMatrixIsSymmetricAndNormalisationGivesUnitDiagonal	Fact	Kernel gram matrix is symmetric and normalisation gives unit diagonal.
KernelGramMatrixGaussianDiagonalIsOneAndInputIsValidated	Fact	Kernel gram matrix gaussian diagonal is one and input is validated.
KernelCrossMatrixIsRectangularAndMatchesTheGramWhenSetsAreEqual	Fact	Kernel cross matrix is rectangular and matches the gram when sets are equal.
HistogramOverlapMatchesClosedForms	Fact	Histogram overlap matches closed forms.
HistogramOverlapRejectsNegativeEmptyAndMismatchedInput	Fact	Histogram overlap rejects negative empty and mismatched input.
GaussianBhattacharyyaEqualsOneEighthOfSquaredMeanShiftForEqualCovariance	Fact	Gaussian bhattacharyya equals one eighth of squared mean shift for equal covariance.
GaussianBhattacharyyaRejectsSmallOrMismatchedSamples	Fact	Gaussian bhattacharyya rejects small or mismatched samples.
StringDistanceMatchesWikipediaExamples	Fact	String distance matches wikipedia examples.
StringDistanceHandlesEmptyStringsAndRejectsBadInput	Fact	String distance handles empty strings and rejects bad input.
ClosestStringMatchesAreRankedNearestFirstWithStableTies	Fact	Closest string matches are ranked nearest first with stable ties.
ClosestStringMatchesRejectsEmptyCandidatesAndBadTop	Fact	Closest string matches rejects empty candidates and bad top.
StringDistanceMatrixIsSymmetric	Fact	String distance matrix is symmetric.
StringDistanceMatrixRejectsEmptyAndNullEntries	Fact	String distance matrix rejects empty and null entries.
TokenSequenceEditDistanceCountsInsertionsDeletionsAndSubstitutions	Fact	Token sequence edit distance counts insertions deletions and substitutions.
TokenSequenceEditDistanceHandlesEmptySequencesAndRejectsNull	Fact	Token sequence edit distance handles empty sequences and rejects null.
TokenSetSimilarityMatchesHandCounts	Fact	Token set similarity matches hand counts.
TokenSetSimilarityHandlesEmptySetsAndRejectsNull	Fact	Token set similarity handles empty sets and rejects null.
SeededRandomScopeRestoresThePreviousThreadSeedAfterAClusteringCall	Fact	Seeded random scope restores the previous thread seed after a clustering call.
KMeansSplitsTwoSquaresAndReportsHandComputedInertiaProfilesAndSilhouette	Fact	K means splits two squares and reports hand computed inertia profiles and silhouette.
KMeansIsRepeatableForASeedAndReportsCentroidsInOriginalUnitsWhenStandardised	Fact	K means is repeatable for a seed and reports centroids in original units when standardised.
KMeansHandlesSingleClusterAndRejectsBadArguments	Fact	K means handles single cluster and rejects bad arguments.
MiniBatchKMeansSeparatesWellSeparatedBlobs	Fact	Mini batch k means separates well separated blobs.
MiniBatchKMeansRejectsBadBatchSize	Fact	Mini batch k means rejects bad batch size.
BinarySplitSeparatesTwoSquares	Fact	Binary split separates two squares.
BinarySplitRejectsBadArguments	Fact	Binary split rejects bad arguments.
BalancedKMeansGivesEqualSizedClusters	Fact	Balanced k means gives equal sized clusters.
BalancedKMeansRejectsTooManyRowsAndClusters	Fact	Balanced k means rejects too many rows and clusters.
KMedoidsUsesActualRowsAsCentres	Fact	K medoids uses actual rows as centres.
KMedoidsSupportsOtherSeedingAndRejectsBadInput	Fact	K medoids supports other seeding and rejects bad input.
KModesFindsCategoricalModesAndCountsMismatches	Fact	K modes finds categorical modes and counts mismatches.
KModesRejectsRaggedEmptyAndTooManyClusters	Fact	K modes rejects ragged empty and too many clusters.
MeanShiftDiscoversTheNumberOfClusters	Fact	Mean shift discovers the number of clusters.
MeanShiftSupportsGaussianKernelAndRejectsBadBandwidth	Fact	Mean shift supports gaussian kernel and rejects bad bandwidth.
GaussianMixtureRecoversTwoBlobsAndReportsConsistentInformationCriteria	Fact	Gaussian mixture recovers two blobs and reports consistent information criteria.
GaussianMixtureDiagonalCountsFewerParametersAndValidatesInput	Fact	Gaussian mixture diagonal counts fewer parameters and validates input.
MixtureSelectionPrefersTwoComponentsForTwoBlobs	Fact	Mixture selection prefers two components for two blobs.
MixtureSelectionRejectsBadRange	Fact	Mixture selection rejects bad range.
MixtureAnomalyDetectionFlagsAPointFarFromEveryComponent	Fact	Mixture anomaly detection flags a point far from every component.
MixtureAnomalyDetectionScoresReferenceRowsByDefaultAndValidatesContamination	Fact	Mixture anomaly detection scores reference rows by default and validates contamination.
KMeansPlusPlusSeedsAreDistinctRepeatableRealRows	Fact	K means plus plus seeds are distinct repeatable real rows.
KMeansPlusPlusSeedsRejectBadCount	Fact	K means plus plus seeds reject bad count.
SilhouetteMatchesHandComputationForTwoSquares	Fact	Silhouette matches hand computation for two squares.
SilhouetteScoresSingletonsZeroAndFlagsMisassignedRowsNegative	Fact	Silhouette scores singletons zero and flags misassigned rows negative.
DaviesBouldinIsOneTenthForTwoSquares	Fact	Davies bouldin is one tenth for two squares.
DaviesBouldinIsWorseForAScrambledLabelling	Fact	Davies bouldin is worse for a scrambled labelling.
CalinskiHarabaszIsSixHundredForTwoSquares	Fact	Calinski harabasz is six hundred for two squares.
CalinskiHarabaszIsInfiniteWhenClustersAreDegenerateAndNanWhenEveryRowIsAlone	Fact	Calinski harabasz is infinite when clusters are degenerate and nan when every row is alone.
QualitySummaryCombinesTheHandComputedMeasures	Fact	Quality summary combines the hand computed measures.
QualitySummaryRejectsSingleClusterAndMismatchedLabels	Fact	Quality summary rejects single cluster and mismatched labels.
ElbowTableIsMonotoneInInertiaAndAllMeasuresPreferTwoForTwoSquares	Fact	Elbow table is monotone in inertia and all measures prefer two for two squares.
ElbowTableRejectsBadRanges	Fact	Elbow table rejects bad ranges.
GapStatisticFindsTwoClustersInTwoBlobsAndIsRepeatable	Fact	Gap statistic finds two clusters in two blobs and is repeatable.
GapStatisticRejectsBadArguments	Fact	Gap statistic rejects bad arguments.
ProfilingReportsCentroidsSpreadAndStandardisedDifferences	Fact	Profiling reports centroids spread and standardised differences.
ProfilingHandlesConstantColumnsSingletonsAndBadNames	Fact	Profiling handles constant columns singletons and bad names.
AssignmentPicksTheNearestCentroidAndReportsAllDistances	Fact	Assignment picks the nearest centroid and reports all distances.
AssignmentRejectsMismatchedColumnsAndEmptyCentroids	Fact	Assignment rejects mismatched columns and empty centroids.
ClusterAgreementMatchesHandCountedPairs	Fact	Cluster agreement matches hand counted pairs.
ClusterAgreementHandlesTrivialPartitionsAndRejectsBadInput	Fact	Cluster agreement handles trivial partitions and rejects bad input.
KNearestNeighboursAgreeAcrossEveryIndexForAQuery	Theory	K nearest neighbours agree across every index for a query.
KNearestNeighboursExcludeTheRowItselfWhenQueriesAreTheReference	Theory	K nearest neighbours exclude the row itself when queries are the reference.
KNearestNeighboursHonourTheMetricAndMatchBruteForceOnRandomData	Fact	K nearest neighbours honour the metric and match brute force on random data.
KNearestNeighboursRejectBadArguments	Fact	K nearest neighbours reject bad arguments.
RadiusSearchReturnsEveryRowWithinTheRadiusNearestFirst	Fact	Radius search returns every row within the radius nearest first.
RadiusSearchRejectsBadRadiusAndCap	Fact	Radius search rejects bad radius and cap.
NeighbourClassificationVotesAmongTheNearestLabelledRows	Fact	Neighbour classification votes among the nearest labelled rows.
NeighbourClassificationRejectsBadArguments	Fact	Neighbour classification rejects bad arguments.
NearestNeighbourOutliersFlagOnlyTheIsolatedRow	Fact	Nearest neighbour outliers flag only the isolated row.
NearestNeighbourOutliersRejectBadArguments	Fact	Nearest neighbour outliers reject bad arguments.
AssociationRulesReproduceTheTextbookMarketBasketExample	Fact	Association rules reproduce the textbook market basket example.
AssociationRulesRespectConfidenceAndCapsAndIgnoreRepeatedItems	Fact	Association rules respect confidence and caps and ignore repeated items.
AssociationRulesRejectBadInputAndUnboundedSizes	Fact	Association rules reject bad input and unbounded sizes.
PrincipalComponentAnalysisReproducesTheSmithTutorialEigenAnalysis	Fact	Principal component analysis reproduces the smith tutorial eigen analysis.
PrincipalComponentAnalysisScoresAreProjectionsWithNormalisedSign	Fact	Principal component analysis scores are projections with normalised sign.
PrincipalComponentAnalysisOfPerfectlyCorrelatedDataHasOneComponent	Fact	Principal component analysis of perfectly correlated data has one component.
PrincipalComponentAnalysisOnTheCorrelationBasisIgnoresColumnScale	Fact	Principal component analysis on the correlation basis ignores column scale.
PrincipalComponentAnalysisRejectsBadInputWithExplanations	Fact	Principal component analysis rejects bad input with explanations.
InterpretPrincipalComponentsListsLargestLoadingsAndCommunalities	Fact	Interpret principal components lists largest loadings and communalities.
InterpretPrincipalComponentsDefaultsNamesAndRejectsBadNames	Fact	Interpret principal components defaults names and rejects bad names.
ProjectingNewRowsUsesTheReferenceMeansAndComponents	Fact	Projecting new rows uses the reference means and components.
ProjectingNewRowsRejectsColumnMismatchAndNan	Fact	Projecting new rows rejects column mismatch and nan.
WhiteningGivesUncorrelatedUnitVarianceColumns	Fact	Whitening gives uncorrelated unit variance columns.
WhiteningDropsNegligibleComponentsOfCollinearData	Fact	Whitening drops negligible components of collinear data.
DiagnosticsMatchHandComputedHotellingAndPredictionError	Fact	Diagnostics match hand computed hotelling and prediction error.
DiagnosticsFlagAFarAwayRowAndValidateInput	Fact	Diagnostics flag a far away row and validate input.
ReconstructionFromOneComponentMatchesHandProjectionAndIsExactForCollinearData	Fact	Reconstruction from one component matches hand projection and is exact for collinear data.
ReconstructionScoresNewRowsAndRejectsBadInput	Fact	Reconstruction scores new rows and rejects bad input.
KernelPrincipalComponentAnalysisWithLinearKernelMatchesOrdinaryScores	Fact	Kernel principal component analysis with linear kernel matches ordinary scores.
KernelPrincipalComponentAnalysisWithGaussianKernelSeparatesTwoBlobsOnTheFirstComponent	Fact	Kernel principal component analysis with gaussian kernel separates two blobs on the first component.
KernelPrincipalComponentAnalysisRejectsBadKernelParametersAndSize	Fact	Kernel principal component analysis rejects bad kernel parameters and size.
IndependentComponentAnalysisRecoversMixedUniformSources	Fact	Independent component analysis recovers mixed uniform sources.
IndependentComponentAnalysisIsRepeatableForAFixedSeedAndValidatesInput	Fact	Independent component analysis is repeatable for a fixed seed and validates input.
LinearDiscriminantAnalysisSeparatesTwoSymmetricClasses	Fact	Linear discriminant analysis separates two symmetric classes.
LinearDiscriminantAnalysisWithThreeClassesReturnsTwoDirections	Fact	Linear discriminant analysis with three classes returns two directions.
LinearDiscriminantAnalysisRejectsBadLabels	Fact	Linear discriminant analysis rejects bad labels.
KernelDiscriminantAnalysisSeparatesTwoBlobs	Fact	Kernel discriminant analysis separates two blobs.
KernelDiscriminantAnalysisValidatesRegularisationAndLabels	Fact	Kernel discriminant analysis validates regularisation and labels.
LinearDiscriminantClassificationAssignsToTheNearestProjectedClassMean	Fact	Linear discriminant classification assigns to the nearest projected class mean.
LinearDiscriminantClassificationRejectsMismatchedColumns	Fact	Linear discriminant classification rejects mismatched columns.
MahalanobisDistancesMatchHandComputationOnTheUnitCross	Fact	Mahalanobis distances match hand computation on the unit cross.
MahalanobisOutlierDetectionFlagsAnInjectedOutlierAndUsesPseudoInverseForCollinearData	Fact	Mahalanobis outlier detection flags an injected outlier and uses pseudo inverse for collinear data.
ScoringAgainstReferenceUsesOnlyTheReferenceCentreAndCovariance	Fact	Scoring against reference uses only the reference centre and covariance.
ScoringAgainstReferenceRejectsMismatchAndTinyReference	Fact	Scoring against reference rejects mismatch and tiny reference.
TsneKeepsTwoSeparatedClustersApartAndIsRepeatableForASeed	Fact	Tsne keeps two separated clusters apart and is repeatable for a seed.
TsneSupportsThreeDimensionsAndRejectsBadInput	Fact	Tsne supports three dimensions and rejects bad input.

NumericsAndOptimisationCalculusAndRootFindingToolsTests

Jube.Test.AdvancedAnalytics.Statistics.NumericsAndOptimisationCalculusAndRootFindingToolsTests — 22 tests.

Test	Kind	Verifies
EvaluateNamedFunctionEveryFamily	Fact	Evaluate named function every family.
IntegrateTrapezoidalRuleKnownIntegrals	Fact	Integrate trapezoidal rule known integrals.
IntegrateRombergKnownIntegrals	Fact	Integrate romberg known integrals.
IntegrateGaussKronrodKnownIntegralsAndErrorEstimate	Fact	Integrate gauss kronrod known integrals and error estimate.
IntegrateAdaptiveGaussKronrodInfiniteKnownIntegrals	Fact	Integrate adaptive gauss kronrod infinite known integrals.
IntegrateMonteCarloOnIntervalIsWithinStandardErrorAndReproducible	Fact	Integrate monte carlo on interval is within standard error and reproducible.
IntegrateMonteCarloObjectiveOverBoxKnownIntegral	Fact	Integrate monte carlo objective over box known integral.
NumericalDerivativeOfNamedFunctionKnownDerivatives	Fact	Numerical derivative of named function known derivatives.
NumericalGradientOfObjectiveKnownGradients	Fact	Numerical gradient of objective known gradients.
NumericalHessianOfObjectiveKnownHessians	Fact	Numerical hessian of objective known hessians.
NumericalJacobianOfVectorFunctionKnownJacobians	Fact	Numerical jacobian of vector function known jacobians.
FindRootBrentKnownRoots	Fact	Find root brent known roots.
FindRootBracketsByScanningFindsSineZeros	Fact	Find root brackets by scanning finds sine zeros.
FindExtremumBrentKnownExtrema	Fact	Find extremum brent known extrema.
EvaluatePolynomialHorner	Fact	Evaluate polynomial horner.
PolynomialDerivativeOrAntiderivativeKnownAnswers	Fact	Polynomial derivative or antiderivative known answers.
PolynomialMultiplyKnownProduct	Fact	Polynomial multiply known product.
PolynomialRootsKnownRoots	Fact	Polynomial roots known roots.
FitPolynomialByLeastSquaresKnownFits	Fact	Fit polynomial by least squares known fits.
InterpolatePolynomialThroughPointsRecoversQuadratic	Fact	Interpolate polynomial through points recovers quadratic.
InterpolateLinearlyKnownValues	Fact	Interpolate linearly known values.
ExtrapolateLinearlyExtendsEndSegments	Fact	Extrapolate linearly extends end segments.

NumericsAndOptimisationCombinatoricsAndUtilityToolsTests

Jube.Test.AdvancedAnalytics.Statistics.NumericsAndOptimisationCombinatoricsAndUtilityToolsTests — 27 tests.

Test	Kind	Verifies
EnumeratePermutationsListsEveryOrdering	Fact	Enumerate permutations lists every ordering.
EnumerateCombinationsListsEverySelection	Fact	Enumerate combinations lists every selection.
EnumerateSubsetsListsPowerSet	Fact	Enumerate subsets lists power set.
EnumerateSequencesListsCartesianPower	Fact	Enumerate sequences lists cartesian power.
GenerateTruthTableEnumeratesAllBooleanCombinations	Fact	Generate truth table enumerates all boolean combinations.
CountCombinatorialObjectsKnownCounts	Fact	Count combinatorial objects known counts.
GreatestCommonDivisorAndLeastCommonMultipleKnownValues	Fact	Greatest common divisor and least common multiple known values.
EuclideanModuloWrapsIntoRange	Fact	Euclidean modulo wraps into range.
PowerOfTwoPropertiesKnownValues	Fact	Power of two properties known values.
FindIntegerByBinarySearchFindsSquareRoot	Fact	Find integer by binary search finds square root.
SortValuesWithOriginalIndicesIsStableAndReportsOrigin	Fact	Sort values with original indices is stable and reports origin.
SortValuesByKeysReordersInParallel	Fact	Sort values by keys reorders in parallel.
SelectNthSmallestValueKnownRanks	Fact	Select nth smallest value known ranks.
SelectSmallestValuesSortedKnownTopN	Fact	Select smallest values sorted known top n.
GenerateUniformRandomNumbersIsReproducibleAndInRange	Fact	Generate uniform random numbers is reproducible and in range.
GenerateNormalRandomNumbersHaveRequestedMoments	Fact	Generate normal random numbers have requested moments.
GenerateExponentialRandomNumbersHaveRequestedMean	Fact	Generate exponential random numbers have requested mean.
MonteCarloExpectationOfNamedFunctionMatchesClosedForms	Fact	Monte carlo expectation of named function matches closed forms.
MonteCarloProbabilityOfNamedFunctionMatchesNormalTables	Fact	Monte carlo probability of named function matches normal tables.
GetMathematicalConstantsHasKnownValues	Fact	Get mathematical constants has known values.
NumericsFastFourierTransformKnownTransformAndRoundTrip	Fact	Numerics fast fourier transform known transform and round trip.
NumericsDiscreteCosineTransformKnownValuesAndRoundTrip	Fact	Numerics discrete cosine transform known values and round trip.
NumericsDiscreteSineTransformRoundTrip	Fact	Numerics discrete sine transform round trip.
NumericsHartleyTransformKnownValuesAndSelfInverse	Fact	Numerics hartley transform known values and self inverse.
NumericsHilbertTransformOfCosineIsSine	Fact	Numerics hilbert transform of cosine is sine.
NumericsHaarWaveletTransformKnownValuesAndRoundTrip	Fact	Numerics haar wavelet transform known values and round trip.
NumericsCdf97WaveletTransformRoundTripAndSmoothness	Fact	Numerics cdf97 wavelet transform round trip and smoothness.

NumericsAndOptimisationLinearAlgebraToolsTests

Jube.Test.AdvancedAnalytics.Statistics.NumericsAndOptimisationLinearAlgebraToolsTests — 28 tests.

Test	Kind	Verifies
MatrixMultiplyKnownProductAndShapeChecks	Fact	Matrix multiply known product and shape checks.
MatrixVectorMultiplyKnownProduct	Fact	Matrix vector multiply known product.
MatrixTransposeSwapsRowsAndColumns	Fact	Matrix transpose swaps rows and columns.
MatrixElementwiseOperationAllOperations	Fact	Matrix elementwise operation all operations.
MatrixInverseKnownAnswerAndSingularRejected	Fact	Matrix inverse known answer and singular rejected.
MatrixPseudoInverseMatchesPublishedMoorePenroseExample	Fact	Matrix pseudo inverse matches published moore penrose example.
MatrixDeterminantKnownAnswers	Fact	Matrix determinant known answers.
MatrixPseudoDeterminantIsProductOfNonZeroSingularValues	Fact	Matrix pseudo determinant is product of non zero singular values.
MatrixTraceSumsDiagonal	Fact	Matrix trace sums diagonal.
MatrixRankAndConditionKnownAnswers	Fact	Matrix rank and condition known answers.
MatrixNormsMatchDefinitions	Fact	Matrix norms match definitions.
VectorNormsThreeFourFive	Fact	Vector norms three four five.
SolveLinearSystemKnownSolution	Fact	Solve linear system known solution.
SolveLinearSystemMultipleRightHandSidesKnownSolution	Fact	Solve linear system multiple right hand sides known solution.
SolveLeastSquaresFitsLineExactAndApproximate	Fact	Solve least squares fits line exact and approximate.
MatrixNullSpaceVectorsAreOrthonormalAndAnnihilateTheMatrix	Fact	Matrix null space vectors are orthonormal and annihilate the matrix.
MatrixReducedRowEchelonFormKnownAnswers	Fact	Matrix reduced row echelon form known answers.
MatrixKroneckerProductMatchesReferenceExample	Fact	Matrix kronecker product matches reference example.
VectorOuterProductKnownAnswer	Fact	Vector outer product known answer.
VectorDotProductKnownAnswerAndLengthMismatch	Fact	Vector dot product known answer and length mismatch.
VectorCrossProductKnownAnswers	Fact	Vector cross product known answers.
MatrixStructurePropertiesClassifiesMatrices	Fact	Matrix structure properties classifies matrices.
GenerateStructuredMatrixKinds	Fact	Generate structured matrix kinds.
MatrixPowerGivesFibonacciNumbers	Fact	Matrix power gives fibonacci numbers.
GenerateMeshGridEnumeratesPoints	Fact	Generate mesh grid enumerates points.
GenerateEvenlySpacedValuesIncludesBothEnds	Fact	Generate evenly spaced values includes both ends.
NumericsConvolveVectorsKnownConvolution	Fact	Numerics convolve vectors known convolution.
RescaleValuesToRangeMapsLinearly	Fact	Rescale values to range maps linearly.

NumericsAndOptimisationMatrixDecompositionToolsTests

Jube.Test.AdvancedAnalytics.Statistics.NumericsAndOptimisationMatrixDecompositionToolsTests — 10 tests.

Test	Kind	Verifies
LuDecompositionReconstructsPermutedInput	Fact	Lu decomposition reconstructs permuted input.
QrDecompositionReconstructsAndIsOrthonormal	Fact	Qr decomposition reconstructs and is orthonormal.
CholeskyDecompositionMatchesPublishedExample	Fact	Cholesky decomposition matches published example.
SolveSymmetricPositiveDefiniteSystemKnownSolution	Fact	Solve symmetric positive definite system known solution.
SingularValueDecompositionMatchesPublishedValuesAndReconstructs	Fact	Singular value decomposition matches published values and reconstructs.
SymmetricEigenDecompositionKnownEigenpairs	Fact	Symmetric eigen decomposition known eigenpairs.
GeneralEigenDecompositionRealAndComplexCases	Fact	General eigen decomposition real and complex cases.
GeneralizedEigenDecompositionScalesWithB	Fact	Generalized eigen decomposition scales with b.
GramSchmidtOrthogonalisationReconstructs	Fact	Gram schmidt orthogonalisation reconstructs.
NonnegativeMatrixFactorisationRecoversRankOneMatrixAndIsSeedDeterministic	Fact	Nonnegative matrix factorisation recovers rank one matrix and is seed deterministic.

NumericsAndOptimisationOptimisationToolsTests

Jube.Test.AdvancedAnalytics.Statistics.NumericsAndOptimisationOptimisationToolsTests — 13 tests.

Test	Kind	Verifies
EvaluateNamedObjectiveKnownValuesAtKnownMinima	Fact	Evaluate named objective known values at known minima.
MinimiseWithLimitedMemoryBfgsFindsKnownMinima	Fact	Minimise with limited memory bfgs finds known minima.
MinimiseWithBoundedBfgsRespectsBounds	Fact	Minimise with bounded bfgs respects bounds.
MinimiseWithConjugateGradientFindsKnownMinima	Fact	Minimise with conjugate gradient finds known minima.
MinimiseWithGradientDescentConvergesOnConvexProblemsAndRejectsBadRates	Fact	Minimise with gradient descent converges on convex problems and rejects bad rates.
MinimiseWithNelderMeadFindsKnownMinimaDerivativeFree	Fact	Minimise with nelder mead finds known minima derivative free.
MinimiseWithSubplexFindsKnownMinima	Fact	Minimise with subplex finds known minima.
CompareUnconstrainedOptimisersAgreeOnConvexProblem	Fact	Compare unconstrained optimisers agree on convex problem.
SolveQuadraticProgramMatchesTextbookExamples	Fact	Solve quadratic program matches textbook examples.
MinimiseWithLinearConstraintsCobylaMatchesQuadraticProgram	Fact	Minimise with linear constraints cobyla matches quadratic program.
SolveLinearProgramMatchesTextbookExamples	Fact	Solve linear program matches textbook examples.
FitNamedCurveLeastSquaresRecoversKnownCurves	Fact	Fit named curve least squares recovers known curves.
SolveAssignmentProblemMunkresKnownAssignments	Fact	Solve assignment problem munkres known assignments.

NumericsAndOptimisationSpecialFunctionToolsTests

Jube.Test.AdvancedAnalytics.Statistics.NumericsAndOptimisationSpecialFunctionToolsTests — 32 tests.

Test	Kind	Verifies
GammaFunctionKnownValues	Fact	Gamma function known values.
LogGammaFunctionKnownValuesAndLargeArguments	Fact	Log gamma function known values and large arguments.
DigammaFunctionKnownValues	Fact	Digamma function known values.
TrigammaFunctionKnownValues	Fact	Trigamma function known values.
MultivariateGammaFunctionMatchesClosedForm	Fact	Multivariate gamma function matches closed form.
RegularisedLowerIncompleteGammaClosedForms	Fact	Regularised lower incomplete gamma closed forms.
RegularisedUpperIncompleteGammaClosedForms	Fact	Regularised upper incomplete gamma closed forms.
InverseRegularisedIncompleteGammaInvertsClosedForm	Fact	Inverse regularised incomplete gamma inverts closed form.
BetaFunctionKnownValues	Fact	Beta function known values.
MultinomialBetaFunctionReducesToBeta	Fact	Multinomial beta function reduces to beta.
RegularisedIncompleteBetaClosedForms	Fact	Regularised incomplete beta closed forms.
InverseRegularisedIncompleteBetaInvertsClosedForms	Fact	Inverse regularised incomplete beta inverts closed forms.
ErrorFunctionFamilyKnownValues	Fact	Error function family known values.
StandardNormalFunctionKnownValues	Fact	Standard normal function known values.
BivariateNormalCdfKnownValues	Fact	Bivariate normal cdf known values.
OwensTFunctionKnownValues	Fact	Owens t function known values.
BesselFunctionKnownValues	Fact	Bessel function known values.
FactorialFunctionKnownValuesAndBounds	Fact	Factorial function known values and bounds.
BinomialCoefficientKnownValues	Fact	Binomial coefficient known values.
LogSumExpIsStable	Fact	Log sum exp is stable.
SoftmaxProbabilitiesSumToOneAndMatchKnownValues	Fact	Softmax probabilities sum to one and match known values.
SigmoidAndLogitInvertEachOther	Fact	Sigmoid and logit invert each other.
StableLogExpFunctionsKeepPrecisionNearZero	Fact	Stable log exp functions keep precision near zero.
LogAddAndSubtractPairsKnownValues	Fact	Log add and subtract pairs known values.
ReciprocalAndInverseHyperbolicFunctionsKnownValues	Fact	Reciprocal and inverse hyperbolic functions known values.
StirlingGammaApproximationIsCloseForLargeArguments	Fact	Stirling gamma approximation is close for large arguments.
GaussianBellFunctionMatchesNormalDensity	Fact	Gaussian bell function matches normal density.
GaussianKernelWeightsAreSymmetricAndPeakAtCentre	Fact	Gaussian kernel weights are symmetric and peak at centre.
TaylorSeriesApproximationConvergesToTrueValues	Fact	Taylor series approximation converges to true values.
BSplineBasisFunctionKnownValues	Fact	B spline basis function known values.
StableHypotenuseHandlesHugeMagnitudes	Fact	Stable hypotenuse handles huge magnitudes.
PlanarAngleKnownQuadrants	Fact	Planar angle known quadrants.

RelationshipsAndRegressionCorrelationTests

Jube.Test.AdvancedAnalytics.Statistics.RelationshipsAndRegressionCorrelationTests — 28 tests.

Test	Kind	Verifies
PearsonMatchesAnscombeQuartetOne	Fact	Pearson matches anscombe quartet one.
PearsonEdgeCases	Fact	Pearson edge cases.
SpearmanMatchesTheClosedFormOnAnscombeQuartetOne	Fact	Spearman matches the closed form on anscombe quartet one.
SpearmanIsInvariantToMonotoneTransformsAndHandlesTies	Fact	Spearman is invariant to monotone transforms and handles ties.
KendallCountsMatchTheHandCountOnAnscombeQuartetOne	Fact	Kendall counts match the hand count on anscombe quartet one.
KendallHandlesTiesAndVariants	Fact	Kendall handles ties and variants.
PointBiserialMatchesTheHandComputation	Fact	Point biserial matches the hand computation.
PointBiserialRejectsBadFlagsAndMissing	Fact	Point biserial rejects bad flags and missing.
BiserialMatchesTheHandComputation	Fact	Biserial matches the hand computation.
CorrelationMatrixAgreesWithThePairwiseToolsAndRanksPairs	Fact	Correlation matrix agrees with the pairwise tools and ranks pairs.
CorrelationMatrixHandlesMissingAndConstantColumns	Fact	Correlation matrix handles missing and constant columns.
CovarianceMatrixMatchesTheClosedForm	Fact	Covariance matrix matches the closed form.
CovarianceMatrixEdgeCases	Fact	Covariance matrix edge cases.
PartialCorrelationMatchesTheFirstOrderFormula	Fact	Partial correlation matches the first order formula.
PartialCorrelationEdgeCases	Fact	Partial correlation edge cases.
SemiPartialCorrelationMatchesTheFirstOrderFormula	Fact	Semi partial correlation matches the first order formula.
PartialCorrelationMatrixMatchesThePartialCorrelationTool	Fact	Partial correlation matrix matches the partial correlation tool.
PartialCorrelationMatrixRejectsCollinearAndSmallInputs	Fact	Partial correlation matrix rejects collinear and small inputs.
MutualInformationOfAFunctionalNonLinearRelationEqualsTheEntropyOfTheOutput	Fact	Mutual information of a functional non linear relation equals the entropy of the output.
MutualInformationEdgeCases	Fact	Mutual information edge cases.
MutualInformationRankingPutsTheNonLinearDriverFirst	Fact	Mutual information ranking puts the non linear driver first.
CorrelationRankingOrdersByAbsoluteStrengthAndAdjustsPValues	Fact	Correlation ranking orders by absolute strength and adjusts p values.
CorrelationRatioMatchesTheOneWayAnovaClosedForm	Fact	Correlation ratio matches the one way anova closed form.
CorrelationRatioEdgeCases	Fact	Correlation ratio edge cases.
CompareIndependentCorrelationsMatchesTheFisherClosedForm	Fact	Compare independent correlations matches the fisher closed form.
CompareIndependentCorrelationsRejectsBadInput	Fact	Compare independent correlations rejects bad input.
CorrelationSummaryIntervalMatchesTheCriticalValueTable	Fact	Correlation summary interval matches the critical value table.
CorrelationSummaryIntervalRejectsBadInput	Fact	Correlation summary interval rejects bad input.

RelationshipsAndRegressionCurveTests

Jube.Test.AdvancedAnalytics.Statistics.RelationshipsAndRegressionCurveTests — 7 tests.

Test	Kind	Verifies
EveryFamilyRecoversItsGeneratingParametersFromNoiseFreeData	Theory	Every family recovers its generating parameters from noise free data.
MichaelisMentenMatchesThePublishedPuromycinFit	Fact	Michaelis menten matches the published puromycin fit.
PredictionsUseTheDeltaMethod	Fact	Predictions use the delta method.
FitValidatesItsInputs	Fact	Fit validates its inputs.
FitWarnsWhenParametersAreNotIdentifiable	Fact	Fit warns when parameters are not identifiable.
ComparisonRanksTheSaturatingFamiliesAheadOfUnsuitableOnes	Fact	Comparison ranks the saturating families ahead of unsuitable ones.
ComparisonReportsFamiliesThatCannotBeFittedAndValidates	Fact	Comparison reports families that cannot be fitted and validates.

RelationshipsAndRegressionDiagnosticsTests

Jube.Test.AdvancedAnalytics.Statistics.RelationshipsAndRegressionDiagnosticsTests — 28 tests.

Test	Kind	Verifies
InfluenceMeasuresMatchTheSimpleRegressionClosedForms	Fact	Influence measures match the simple regression closed forms.
InfluenceDfbetasAndPressMatchBruteForceLeaveOneOutRefits	Fact	Influence dfbetas and press match brute force leave one out refits.
InfluenceFlagsTheAnscombeOutlierAndValidates	Fact	Influence flags the anscombe outlier and validates.
DurbinWatsonMatchesTheHandComputedResiduals	Fact	Durbin watson matches the hand computed residuals.
DurbinWatsonSeparatesAlternatingFromSmoothResiduals	Fact	Durbin watson separates alternating from smooth residuals.
BreuschGodfreyMatchesTheAuxiliaryRegressionRecomputedByAnotherTool	Fact	Breusch godfrey matches the auxiliary regression recomputed by another tool.
BreuschGodfreyAcceptsIndependentResidualsAndValidates	Fact	Breusch godfrey accepts independent residuals and validates.
BreuschPaganMatchesTheAuxiliaryRegressionForBothVariants	Fact	Breusch pagan matches the auxiliary regression for both variants.
BreuschPaganAcceptsConstantVarianceAndValidates	Fact	Breusch pagan accepts constant variance and validates.
WhiteMatchesTheAuxiliaryRegressionWithSquaresAndCrossProducts	Fact	White matches the auxiliary regression with squares and cross products.
WhiteRejectsUnusableInput	Fact	White rejects unusable input.
GoldfeldQuandtMatchesTheHandComputedVarianceRatio	Fact	Goldfeld quandt matches the hand computed variance ratio.
GoldfeldQuandtSortsByTheChosenVariableAndValidates	Fact	Goldfeld quandt sorts by the chosen variable and validates.
ResidualNormalityMatchesHandComputedMoments	Fact	Residual normality matches hand computed moments.
ResidualNormalityDistinguishesNormalFromSkewedResiduals	Fact	Residual normality distinguishes normal from skewed residuals.
ResetMatchesTheNestedFTestOnFittedPowers	Fact	Reset matches the nested f test on fitted powers.
ResetAcceptsALinearModelAndValidates	Fact	Reset accepts a linear model and validates.
ChowMatchesTheHandComputedSegmentResiduals	Fact	Chow matches the hand computed segment residuals.
ChowDetectsABreakAndValidates	Fact	Chow detects a break and validates.
VarianceInflationMatchesTheTwoPredictorClosedFormAndLongley	Fact	Variance inflation matches the two predictor closed form and longley.
VarianceInflationHandlesSingleExactlyCollinearAndConstantColumns	Fact	Variance inflation handles single exactly collinear and constant columns.
ConditionIndicesMatchTheTwoColumnClosedForm	Fact	Condition indices match the two column closed form.
ConditionIndicesForOrthogonalAndLongleyDesigns	Fact	Condition indices for orthogonal and longley designs.
ConditionDiagnosticsValidates	Fact	Condition diagnostics validates.
AddedVariablePlotSlopeEqualsTheMultipleRegressionCoefficient	Fact	Added variable plot slope equals the multiple regression coefficient.
AddedVariablePlotValidates	Fact	Added variable plot validates.
AssumptionCheckPassesAWellBehavedModelAndFlagsAProblemModel	Fact	Assumption check passes a well behaved model and flags a problem model.
AssumptionCheckReportsUncomputableChecksAndValidates	Fact	Assumption check reports uncomputable checks and validates.

RelationshipsAndRegressionGeneralisedLinearTests

Jube.Test.AdvancedAnalytics.Statistics.RelationshipsAndRegressionGeneralisedLinearTests — 14 tests.

Test	Kind	Verifies
PoissonMatchesTheDobsonRandomisedTrialFromTheRGlmDocumentation	Fact	Poisson matches the dobson randomised trial from the r glm documentation.
GammaWithInverseLinkMatchesTheMcCullaghNelderClottingData	Fact	Gamma with inverse link matches the mc cullagh nelder clotting data.
GaussianIdentityEqualsOrdinaryLeastSquares	Fact	Gaussian identity equals ordinary least squares.
BinomialLogitMatchesTheBlissBeetleCoefficients	Fact	Binomial logit matches the bliss beetle coefficients.
GlmOptionsOffsetsWeightsDispersionAndValidation	Fact	Glm options offsets weights dispersion and validation.
PerfectSeparationIsReportedNotHidden	Fact	Perfect separation is reported not hidden.
PoissonRegressionMatchesTheDobsonFitAndHandlesExposure	Fact	Poisson regression matches the dobson fit and handles exposure.
GammaRegressionMatchesTheClottingDataAndLogLinkIsPositive	Fact	Gamma regression matches the clotting data and log link is positive.
ProbitMatchesTheBlissBeetleCoefficientsAndTheGenericFit	Fact	Probit matches the bliss beetle coefficients and the generic fit.
ComplementaryLogLogMatchesTheBlissBeetleCoefficients	Fact	Complementary log log matches the bliss beetle coefficients.
PredictionUsesTheInverseLinkAndTheLinkScaleInterval	Fact	Prediction uses the inverse link and the link scale interval.
PredictionKeepsProbabilitiesInRangeAndValidatesOffsets	Fact	Prediction keeps probabilities in range and validates offsets.
LinkFunctionsMatchTheirClosedForms	Fact	Link functions match their closed forms.
LinkFunctionsFlagValuesOutsideTheirDomain	Fact	Link functions flag values outside their domain.

RelationshipsAndRegressionLinearTests

Jube.Test.AdvancedAnalytics.Statistics.RelationshipsAndRegressionLinearTests — 30 tests.

Test	Kind	Verifies
SimpleRegressionMatchesTheClosedFormAndPublishedAnscombeFigures	Fact	Simple regression matches the closed form and published anscombe figures.
SimpleRegressionOptionsAndEdgeCases	Fact	Simple regression options and edge cases.
MultipleRegressionReproducesTheNistLongleyCertifiedValues	Fact	Multiple regression reproduces the nist longley certified values.
MultipleRegressionReportsVarianceInflationForCollinearPredictors	Fact	Multiple regression reports variance inflation for collinear predictors.
MultipleRegressionValidatesItsInput	Fact	Multiple regression validates its input.
WeightedRegressionMatchesTheWeightedClosedForm	Fact	Weighted regression matches the weighted closed form.
WeightedRegressionRejectsBadWeights	Fact	Weighted regression rejects bad weights.
PolynomialRegressionRecoversAnExactQuadraticAndIsInvariantToCentring	Fact	Polynomial regression recovers an exact quadratic and is invariant to centring.
PolynomialDegreeOneEqualsSimpleRegressionAndValidates	Fact	Polynomial degree one equals simple regression and validates.
DegreeSelectionFindsTheTrueQuadratic	Fact	Degree selection finds the true quadratic.
DegreeSelectionMarksUnfittableDegreesAndValidates	Fact	Degree selection marks unfittable degrees and validates.
PredictionIntervalsMatchTheClosedForm	Fact	Prediction intervals match the closed form.
PredictionValidatesItsInputs	Fact	Prediction validates its inputs.
NestedComparisonOfOneVariableEqualsTheSquaredTStatistic	Fact	Nested comparison of one variable equals the squared t statistic.
NestedComparisonOfSeveralVariablesMatchesThePartialFFormula	Fact	Nested comparison of several variables matches the partial f formula.
NestedComparisonRejectsBadNames	Fact	Nested comparison rejects bad names.
MultivariateRegressionMatchesSeparateFits	Fact	Multivariate regression matches separate fits.
MultivariateRegressionValidates	Fact	Multivariate regression validates.
RidgeMatchesTheSinglePredictorClosedForm	Fact	Ridge matches the single predictor closed form.
RidgeShrinksCollinearCoefficientsAndValidates	Fact	Ridge shrinks collinear coefficients and validates.
RidgePathShrinksMonotonicallyAndPicksTheLowestGcv	Fact	Ridge path shrinks monotonically and picks the lowest gcv.
RidgePathValidates	Fact	Ridge path validates.
NonNegativeLeastSquaresClampsNegativeCoefficientsToZero	Fact	Non negative least squares clamps negative coefficients to zero.
NonNegativeLeastSquaresValidates	Fact	Non negative least squares validates.
RansacFindsTheTrueLineAndTheOutliers	Fact	Ransac finds the true line and the outliers.
RansacIsReproduciblePerSeedAndValidates	Fact	Ransac is reproducible per seed and validates.
PartialLeastSquaresWithAllComponentsEqualsOrdinaryLeastSquares	Fact	Partial least squares with all components equals ordinary least squares.
PartialLeastSquaresValidates	Fact	Partial least squares validates.
LeaveOneOutCrossValidationEqualsTheHatMatrixShortcut	Fact	Leave one out cross validation equals the hat matrix shortcut.
KFoldCrossValidationIsSeededAndValidates	Fact	K fold cross validation is seeded and validates.

RelationshipsAndRegressionSelectionTests

Jube.Test.AdvancedAnalytics.Statistics.RelationshipsAndRegressionSelectionTests — 8 tests.

Test	Kind	Verifies
EveryDirectionSelectsTheTrueSignalsUnderAic	Fact	Every direction selects the true signals under aic.
TheSelectedModelIsALocalAicOptimumAndStepsAreRecorded	Fact	The selected model is a local aic optimum and steps are recorded.
PValueAndBicCriteriaWork	Fact	P value and bic criteria work.
StepwiseValidatesItsInputs	Fact	Stepwise validates its inputs.
BestSubsetMatchesABruteForceOverIndependentFits	Fact	Best subset matches a brute force over independent fits.
BestSubsetSupportsEveryCriterionAndValidates	Fact	Best subset supports every criterion and validates.
InformationCriteriaMatchTheClosedForms	Fact	Information criteria match the closed forms.
InformationCriteriaValidateAndLinkToARegressionFit	Fact	Information criteria validate and link to a regression fit.

TableShapingToolsTests

Jube.Test.AdvancedAnalytics.Statistics.TableShapingToolsTests — 17 tests.

Test	Kind	Verifies
FilterTableRowsKeepsGivenIndicesInGivenOrder	Fact	Filter table rows keeps given indices in given order.
FilterTableRowsOnSingleRowTableKeepsThatRow	Fact	Filter table rows on single row table keeps that row.
FilterTableRowsRejectsEmptyTable	Fact	Filter table rows rejects empty table.
FilterTableRowsRejectsOutOfRangeIndex	Fact	Filter table rows rejects out of range index.
FilterTableRowsRejectsNegativeIndex	Fact	Filter table rows rejects negative index.
DistinctTableRowsKeepsAllRowsWhenAllDistinct	Fact	Distinct table rows keeps all rows when all distinct.
DistinctTableRowsCollapsesAllDuplicatesToOneRow	Fact	Distinct table rows collapses all duplicates to one row.
DistinctTableRowsRejectsOutOfRangeTable	Fact	Distinct table rows rejects out of range table.
ArrangeTableRowsSortsByMultipleKeysWithMixedDirections	Fact	Arrange table rows sorts by multiple keys with mixed directions.
ArrangeTableRowsIsStableWhenEveryKeyTies	Fact	Arrange table rows is stable when every key ties.
ArrangeTableRowsRejectsMismatchedDirectionsLength	Fact	Arrange table rows rejects mismatched directions length.
ArrangeTableRowsRejectsOutOfRangeColumnIndex	Fact	Arrange table rows rejects out of range column index.
RelocateTableColumnsMovesToFrontWhenAfterIsNull	Fact	Relocate table columns moves to front when after is null.
RelocateTableColumnsMovesToEndWhenAfterIsLastRemainingColumn	Fact	Relocate table columns moves to end when after is last remaining column.
RelocateTableColumnsMovesIntoTheMiddle	Fact	Relocate table columns moves into the middle.
RelocateTableColumnsRejectsUnknownColumnName	Fact	Relocate table columns rejects unknown column name.
RelocateTableColumnsRejectsAfterBeingOneOfTheMovedColumns	Fact	Relocate table columns rejects after being one of the moved columns.

TimeSeriesAndSignalToolsTests

Jube.Test.AdvancedAnalytics.Statistics.TimeSeriesAndSignalToolsTests — 219 tests.

Test	Kind	Verifies
CusumAlarmsThreePointsAfterUpwardStepByHandComputation	Fact	Cusum alarms three points after upward step by hand computation.
CusumDetectsDownwardShiftWithEstimatedBaselineAndValidatesConstantBaseline	Fact	Cusum detects downward shift with estimated baseline and validates constant baseline.
PageHinkleyAlarmsOnStepUpAndStepDownByHand	Fact	Page hinkley alarms on step up and step down by hand.
PageHinkleyConstantSeriesIsQuietAndDeltaAbsorbsSmallChange	Fact	Page hinkley constant series is quiet and delta absorbs small change.
EwmaFirstLimitMatchesClosedFormAndTwoSigmaShiftAlarmsAtThirdPoint	Fact	Ewma first limit matches closed form and two sigma shift alarms at third point.
EwmaValidatesParametersAndStaysQuietInControl	Fact	Ewma validates parameters and stays quiet in control.
ShewhartRuleOneFlagsPointBeyondThreeSigma	Fact	Shewhart rule one flags point beyond three sigma.
ShewhartRunRulesTwoThreeAndFour	Fact	Shewhart run rules two three and four.
SpikeDetectionGlobalRobustScoreMatchesHandComputation	Fact	Spike detection global robust score matches hand computation.
SpikeDetectionRollingMethodsFlagSpikeAndDipAgainstQuietHistory	Fact	Spike detection rolling methods flag spike and dip against quiet history.
LevelShiftScanLocatesStepAtIndexTwenty	Fact	Level shift scan locates step at index twenty.
LevelShiftScanFindsNoShiftInStationaryNoiseAndValidatesWindow	Fact	Level shift scan finds no shift in stationary noise and validates window.
MeanShiftFindsTwoChangePointsOfThreeLevelSeries	Fact	Mean shift finds two change points of three level series.
MeanShiftFindsNothingInNoiseHonoursMaxAndValidates	Fact	Mean shift finds nothing in noise honours max and validates.
DrawdownMatchesHandComputedBalanceHistory	Fact	Drawdown matches hand computed balance history.
DrawdownWithoutRecoveryOrWithoutAnyFall	Fact	Drawdown without recovery or without any fall.
AutocorrelationOfOneToFiveMatchesHandComputedBiasedEstimator	Fact	Autocorrelation of one to five matches hand computed biased estimator.
AutocorrelationOfPeriodicSeriesPeaksAtThePeriodAndFlagsSignificantLags	Fact	Autocorrelation of periodic series peaks at the period and flags significant lags.
AutocorrelationEdgeCases	Fact	Autocorrelation edge cases.
PartialAutocorrelationOfOneToFiveMatchesDurbinLevinsonByHand	Fact	Partial autocorrelation of one to five matches durbin levinson by hand.
PartialAutocorrelationOfAutoregressiveSeriesCutsOffAfterLagOne	Fact	Partial autocorrelation of autoregressive series cuts off after lag one.
PartialAutocorrelationConstantSeriesIsNaNAndShortSeriesRejected	Fact	Partial autocorrelation constant series is na n and short series rejected.
CrossCorrelationOfSeriesWithItselfEqualsAutocorrelationByHand	Fact	Cross correlation of series with itself equals autocorrelation by hand.
CrossCorrelationFindsWhichSeriesLeads	Fact	Cross correlation finds which series leads.
CrossCorrelationRejectsMismatchedLengthsAndHandlesConstantSeries	Fact	Cross correlation rejects mismatched lengths and handles constant series.
LjungBoxMatchesClosedFormChiSquareTwoDegreesOfFreedom	Fact	Ljung box matches closed form chi square two degrees of freedom.
LjungBoxRejectsStrongAutocorrelationAndModelDegreesOfFreedomAreSubtracted	Fact	Ljung box rejects strong autocorrelation and model degrees of freedom are subtracted.
BoxPierceMatchesClosedFormChiSquareTwoDegreesOfFreedom	Fact	Box pierce matches closed form chi square two degrees of freedom.
DurbinWatsonOfAlternatingResidualsIsThreeByHand	Fact	Durbin watson of alternating residuals is three by hand.
DurbinWatsonPositiveCorrelationAndAllZeroResiduals	Fact	Durbin watson positive correlation and all zero residuals.
TurningPointTestMatchesHandComputedZScore	Fact	Turning point test matches hand computed z score.
TurningPointTestOfMonotoneSeriesRejectsRandomness	Fact	Turning point test of monotone series rejects randomness.
MedianRunsTestMatchesHandComputedAlternatingCase	Fact	Median runs test matches hand computed alternating case.
MedianRunsTestOfTrendHasTwoRunsAndConstantSeriesIsRejected	Fact	Median runs test of trend has two runs and constant series is rejected.
MannKendallOfPerfectLinearSeriesMatchesHandComputedStatistics	Fact	Mann kendall of perfect linear series matches hand computed statistics.
MannKendallDecreasingTiesAndLimits	Fact	Mann kendall decreasing ties and limits.
AdditiveDecompositionRecoversExactSeasonalPatternAndTrend	Fact	Additive decomposition recovers exact seasonal pattern and trend.
MultiplicativeDecompositionRecoversIndicesAndValidatesInput	Fact	Multiplicative decomposition recovers indices and validates input.
SeasonalityStrengthIsHighForCycleAndLowForNoise	Fact	Seasonality strength is high for cycle and low for noise.
EstimatedPeriodOfSineWithTrendIsTheTruePeriod	Fact	Estimated period of sine with trend is the true period.
EstimatedPeriodNotFoundForConstantOrPureTrendAndRejectsShortInput	Fact	Estimated period not found for constant or pure trend and rejects short input.
ArchLmOfPerfectlyAlternatingSquaresIsRowsTimesOneWithClosedFormPValue	Fact	Arch lm of perfectly alternating squares is rows times one with closed form p value.
ArchLmOfConstantMagnitudeIsNaNAndTooFewRowsRejected	Fact	Arch lm of constant magnitude is na n and too few rows rejected.
GrangerDetectsLaggedCauseAndMatchesIndependentRegression	Fact	Granger detects lagged cause and matches independent regression.
GrangerPerfectFitGivesInfiniteFAndBadInputIsRejected	Fact	Granger perfect fit gives infinite f and bad input is rejected.
NaiveAndDriftForecastsMatchHandComputation	Fact	Naive and drift forecasts match hand computation.
SeasonalNaiveRepeatsLastCycleAndValidatesArguments	Fact	Seasonal naive repeats last cycle and validates arguments.
SimpleSmoothingWithFixedAlphaMatchesHandRecursion	Fact	Simple smoothing with fixed alpha matches hand recursion.
SimpleSmoothingEstimatesAlphaNearOneForRampAndRejectsBadAlpha	Fact	Simple smoothing estimates alpha near one for ramp and rejects bad alpha.
HoltReproducesLinearSeriesExactly	Fact	Holt reproduces linear series exactly.
HoltDampingFlattensTheTrendAndValidates	Fact	Holt damping flattens the trend and validates.
HoltWintersReproducesExactlyPeriodicSeriesAdditiveAndMultiplicative	Fact	Holt winters reproduces exactly periodic series additive and multiplicative.
HoltWintersCapturesTrendPlusSeasonAndValidates	Fact	Holt winters captures trend plus season and validates.
LinearTrendMatchesHandComputedRegressionAndTInterval	Fact	Linear trend matches hand computed regression and t interval.
LinearTrendOfExactLineHasZeroWidthAndNeedsThreePoints	Fact	Linear trend of exact line has zero width and needs three points.
YuleWalkerAndLeastSquaresFitsMatchHandComputationForOneToFive	Fact	Yule walker and least squares fits match hand computation for one to five.
AutoregressiveFitRecoversSimulatedCoefficientAndValidatesOrder	Fact	Autoregressive fit recovers simulated coefficient and validates order.
OrderSelectionFindsOneForArOneAndZeroForNoise	Fact	Order selection finds one for ar one and zero for noise.
YuleWalkerForecastRevertsTowardMeanByHand	Fact	Yule walker forecast reverts toward mean by hand.
LeastSquaresForecastContinuesExactRampAndValidates	Fact	Least squares forecast continues exact ramp and validates.
AccuracyMetricsMatchPublishedRegressionExample	Fact	Accuracy metrics match published regression example.
AccuracyMetricsZeroActualsPerfectForecastAndValidation	Fact	Accuracy metrics zero actuals perfect forecast and validation.
HoldOutComparisonRanksTrendMethodsAboveNaiveOnRamp	Fact	Hold out comparison ranks trend methods above naive on ramp.
HoldOutComparisonUsesSeasonalMethodsForPeriodicSeriesAndValidates	Fact	Hold out comparison uses seasonal methods for periodic series and validates.
DiscreteViterbiMatchesBruteForceEnumerationOfAllPaths	Fact	Discrete viterbi matches brute force enumeration of all paths.
DiscreteDecodeValidatesModelAndObservations	Fact	Discrete decode validates model and observations.
DiscreteLogLikelihoodMatchesBruteForceAndStepProbabilitiesSumToTotal	Fact	Discrete log likelihood matches brute force and step probabilities sum to total.
DiscreteLogLikelihoodImpossibleSymbolIsMinusInfinity	Fact	Discrete log likelihood impossible symbol is minus infinity.
DiscretePosteriorMatchesBruteForceMarginals	Fact	Discrete posterior matches brute force marginals.
DiscretePosteriorOfSingleObservationIsBayesRule	Fact	Discrete posterior of single observation is bayes rule.
DiscreteNextSymbolFollowsFilteredBeliefPushedThroughModel	Fact	Discrete next symbol follows filtered belief pushed through model.
DiscreteNextSymbolRejectsBadInput	Fact	Discrete next symbol rejects bad input.
GaussianViterbiMatchesBruteForceEnumeration	Fact	Gaussian viterbi matches brute force enumeration.
GaussianDecodeValidatesDeviationsAndShapes	Fact	Gaussian decode validates deviations and shapes.
GaussianLogLikelihoodMatchesBruteForce	Fact	Gaussian log likelihood matches brute force.
GaussianLogLikelihoodFlagsOutlierAsMostSurprising	Fact	Gaussian log likelihood flags outlier as most surprising.
GaussianPosteriorMatchesBruteForceMarginals	Fact	Gaussian posterior matches brute force marginals.
GaussianPosteriorOfSingleObservationIsBayesRule	Fact	Gaussian posterior of single observation is bayes rule.
GaussianNextValueMomentsFollowMixtureFormulas	Fact	Gaussian next value moments follow mixture formulas.
GaussianNextValueOfStickySingleRegimeApproachesRegimeMean	Fact	Gaussian next value of sticky single regime approaches regime mean.
DiscreteTrainingRecoversTwoWellSeparatedRegimes	Fact	Discrete training recovers two well separated regimes.
DiscreteTrainingIsDeterministicForSeedAndValidatesArguments	Fact	Discrete training is deterministic for seed and validates arguments.
GaussianTrainingRecoversRegimeMeansDeviationsAndPersistence	Fact	Gaussian training recovers regime means deviations and persistence.
GaussianTrainingSingleRegimeMatchesSampleMomentsAndValidates	Fact	Gaussian training single regime matches sample moments and validates.
StateSelectionPicksTwoRegimesByBicForTwoRegimeData	Fact	State selection picks two regimes by bic for two regime data.
StateSelectionSingleRegimeLogLikelihoodMatchesClosedFormAndValidates	Fact	State selection single regime log likelihood matches closed form and validates.
TransitionMatrixEstimateMatchesHandCountedTable	Fact	Transition matrix estimate matches hand counted table.
TransitionMatrixAbsorbingStateAndMissingExitsAndSmoothing	Fact	Transition matrix absorbing state and missing exits and smoothing.
StationaryDistributionOfTwoStateChainIsFiveSixthsOneSixth	Fact	Stationary distribution of two state chain is five sixths one sixth.
StationaryDistributionPeriodicReducibleAndInvalidMatrices	Fact	Stationary distribution periodic reducible and invalid matrices.
MultiStepProbabilitiesMatchSquaredMatrixByHand	Fact	Multi step probabilities match squared matrix by hand.
MultiStepProbabilitiesZeroStepsLongRunAndValidation	Fact	Multi step probabilities zero steps long run and validation.
SequenceSurpriseMatchesHandComputedSmoothedProbabilities	Fact	Sequence surprise matches hand computed smoothed probabilities.
SequenceSurpriseHandlesNewStatesAndValidation	Fact	Sequence surprise handles new states and validation.
MeanFirstPassageTimesOfTwoStateChainMatchGeometricFormulas	Fact	Mean first passage times of two state chain match geometric formulas.
MeanFirstPassageTimesUnreachableTargetsAreInfinite	Fact	Mean first passage times unreachable targets are infinite.
GamblersRuinAbsorptionMatchesClassicalResults	Fact	Gamblers ruin absorption matches classical results.
AbsorptionAnalysisRejectsChainsWithoutAbsorbingStructure	Fact	Absorption analysis rejects chains without absorbing structure.
DependenceTestOfPerfectlyAlternatingSequenceHasChiSquareEqualToTransitions	Fact	Dependence test of perfectly alternating sequence has chi square equal to transitions.
DependenceTestOfNearIndependentAndDegenerateSequences	Fact	Dependence test of near independent and degenerate sequences.
NGramCountsMatchHandCount	Fact	N gram counts match hand count.
NGramTopKLimitsAndValidation	Fact	N gram top k limits and validation.
EntropyProfileOfAlternatingSequenceHasOneBitAndZeroConditionalEntropy	Fact	Entropy profile of alternating sequence has one bit and zero conditional entropy.
EntropyProfileOfConstantAndCyclicSequences	Fact	Entropy profile of constant and cyclic sequences.
LempelZivClassicExampleHasSixPhrases	Fact	Lempel ziv classic example has six phrases.
LempelZivOfConstantShortAndPeriodicSequences	Fact	Lempel ziv of constant short and periodic sequences.
RunLengthEncodingMatchesHandComputation	Fact	Run length encoding matches hand computation.
RunLengthEncodingSingleSymbolAndValidation	Fact	Run length encoding single symbol and validation.
ThresholdRunsMatchHandComputation	Fact	Threshold runs match hand computation.
ThresholdRunsNaNBreaksStreaksAndNoHits	Fact	Threshold runs na n breaks streaks and no hits.
PiecewiseAggregateApproximationMatchesExactAndFractionalHandComputation	Fact	Piecewise aggregate approximation matches exact and fractional hand computation.
PiecewiseAggregateApproximationBoundaries	Fact	Piecewise aggregate approximation boundaries.
SaxOfLinearRampGivesAbcdWithPublishedBreakpoints	Fact	Sax of linear ramp gives abcd with published breakpoints.
SaxConstantSeriesRawModeAndValidation	Fact	Sax constant series raw mode and validation.
DtwMatchesHandFilledCostMatrix	Fact	Dtw matches hand filled cost matrix.
DtwIdenticalSquaredCostBandAndValidation	Fact	Dtw identical squared cost band and validation.
EditDistanceMatchesHandComputation	Fact	Edit distance matches hand computation.
EditDistanceEmptyAndIdenticalSequences	Fact	Edit distance empty and identical sequences.
FourierTransformOfSampledCosineMatchesClosedForm	Fact	Fourier transform of sampled cosine matches closed form.
FourierTransformOfRampOfLengthFiveMatchesAnalyticFormulaAndScalesFrequencies	Fact	Fourier transform of ramp of length five matches analytic formula and scales frequencies.
InverseFourierTransformRoundTripsForOddAndEvenLengths	Fact	Inverse fourier transform round trips for odd and even lengths.
InverseFourierTransformRejectsMismatchedParts	Fact	Inverse fourier transform rejects mismatched parts.
PowerSpectrumOfUnitCosineOnBinTwoIsNOverTwoAtPeriodEight	Fact	Power spectrum of unit cosine on bin two is n over two at period eight.
PowerSpectrumWindowDetrendAndConstantSeries	Fact	Power spectrum window detrend and constant series.
WelchSpectrumAveragesSevenSegmentsAndFindsPeriodEight	Fact	Welch spectrum averages seven segments and finds period eight.
WelchSpectrumValidatesSegmentAndOverlap	Fact	Welch spectrum validates segment and overlap.
DominantPeriodsRankTwoCyclesWithPowerSharesInAmplitudeSquaredRatio	Fact	Dominant periods rank two cycles with power shares in amplitude squared ratio.
DominantPeriodOfTrendedSeriesAndUnitScaling	Fact	Dominant period of trended series and unit scaling.
SpectralSummaryOfPureCycleIsPeakyAndOfImpulseIsFlat	Fact	Spectral summary of pure cycle is peaky and of impulse is flat.
SpectralSummaryOfConstantSeriesIsUndefined	Fact	Spectral summary of constant series is undefined.
FisherGMatchesClosedFormPValueForNinetyPercentDominance	Fact	Fisher g matches closed form p value for ninety percent dominance.
FisherTestDoesNotFlagNoiseAndConstantIsUndefined	Fact	Fisher test does not flag noise and constant is undefined.
ConvolutionMatchesHandComputedFullSameAndValid	Fact	Convolution matches hand computed full same and valid.
ConvolutionWithMovingAverageKernelSmoothsAndValidatesKernelLength	Fact	Convolution with moving average kernel smooths and validates kernel length.
TemplateMatchFindsExactAndRescaledCopies	Fact	Template match finds exact and rescaled copies.
TemplateMatchConstantWindowsAreNaNAndInputsValidated	Fact	Template match constant windows are na n and inputs validated.
HilbertOfCosineGivesUnitEnvelopeSineQuadratureAndConstantFrequency	Fact	Hilbert of cosine gives unit envelope sine quadrature and constant frequency.
HilbertFrequencyScalesWithSamplingIntervalAndPhaseIsUnwrapped	Fact	Hilbert frequency scales with sampling interval and phase is unwrapped.
DctMatchesClosedFormOrthonormalCoefficients	Fact	Dct matches closed form orthonormal coefficients.
DctInverseRoundTripsAndPreservesEnergy	Fact	Dct inverse round trips and preserves energy.
HaarDecompositionOfFourValuesMatchesHandComputation	Fact	Haar decomposition of four values matches hand computation.
HaarDecompositionRejectsIndivisibleLengthAndConstantHasNoDetail	Fact	Haar decomposition rejects indivisible length and constant has no detail.
HaarDenoiseWithHugeThresholdKeepsOnlyApproximations	Fact	Haar denoise with huge threshold keeps only approximations.
HaarDenoiseZeroThresholdIsLosslessAndUniversalThresholdCleansNoisyStep	Fact	Haar denoise zero threshold is lossless and universal threshold cleans noisy step.
FrequencyFiltersIsolateTheCorrectCosine	Fact	Frequency filters isolate the correct cosine.
FrequencyFilterHighPassRemovesMeanAndValidatesCutoffs	Fact	Frequency filter high pass removes mean and validates cutoffs.
ZeroCrossingsOfAlternatingSeriesAreAtHalfSamples	Fact	Zero crossings of alternating series are at half samples.
ZeroCrossingsAtAnotherLevelAndEdgeCases	Fact	Zero crossings at another level and edge cases.
PeakDetectionMatchesHandComputedPeaksAndProminences	Fact	Peak detection matches hand computed peaks and prominences.
PeakDetectionTroughsPlateausAndNoPeaks	Fact	Peak detection troughs plateaus and no peaks.
ParseIsoTimestampsMatchesKnownUnixTimes	Fact	Parse iso timestamps matches known unix times.
ParseIsoTimestampsNamesTheBadPosition	Fact	Parse iso timestamps names the bad position.
FormatEpochSecondsProducesIsoUtcAndRoundTrips	Fact	Format epoch seconds produces iso utc and round trips.
FormatEpochSecondsRejectsMillisecondsAndNaN	Fact	Format epoch seconds rejects milliseconds and na n.
CalendarFeaturesOfNewYear2021AreAFridayAndHonourOffsets	Fact	Calendar features of new year2021 are a friday and honour offsets.
CalendarFeaturesFlagWeekendAndRejectBadOffset	Fact	Calendar features flag weekend and reject bad offset.
InterArrivalStatisticsMatchHandComputationAndIgnoreInputOrder	Fact	Inter arrival statistics match hand computation and ignore input order.
InterArrivalStatisticsTwoEventsAndDuplicates	Fact	Inter arrival statistics two events and duplicates.
DetectTimeGapsFindsTheLongPauseByMedianMultipleAndAbsoluteThreshold	Fact	Detect time gaps finds the long pause by median multiple and absolute threshold.
DetectTimeGapsRejectsUnsortedInput	Fact	Detect time gaps rejects unsorted input.
ResampleEventsToBucketsCountsSumsAndKeepsEmptyBuckets	Fact	Resample events to buckets counts sums and keeps empty buckets.
ResampleEventsToBucketsHandlesNegativeTimesUnsortedInputAndLimits	Fact	Resample events to buckets handles negative times unsorted input and limits.
TrailingWindowVelocityUsesHalfOpenWindowsByHand	Fact	Trailing window velocity uses half open windows by hand.
TrailingWindowVelocityDuplicateTimestampsAndValidation	Fact	Trailing window velocity duplicate timestamps and validation.
MultiWindowVelocityCountsEachWindowAtTheSnapshotTime	Fact	Multi window velocity counts each window at the snapshot time.
MultiWindowVelocityBeforeAnyEventAndBadWindows	Fact	Multi window velocity before any event and bad windows.
RateChangeMatchesClosedFormPoissonTail	Fact	Rate change matches closed form poisson tail.
RateChangeSilentBaselineAndDecrease	Fact	Rate change silent baseline and decrease.
BurstDetectionFindsTwoBurstsByHand	Fact	Burst detection finds two bursts by hand.
BurstDetectionFindsNothingInRegularStreamAndValidates	Fact	Burst detection finds nothing in regular stream and validates.
SessionizeSplitsOnGapsLongerThanTimeout	Fact	Sessionize splits on gaps longer than timeout.
SessionizeGapEqualToTimeoutStaysInSession	Fact	Sessionize gap equal to timeout stays in session.
HourProfileOfUniformDayHasMaximumEntropyAndZeroChiSquare	Fact	Hour profile of uniform day has maximum entropy and zero chi square.
CalendarProfileConcentratedActivityAndOtherCycles	Fact	Calendar profile concentrated activity and other cycles.
PeriodicityOfClockworkEventsIsPerfect	Fact	Periodicity of clockwork events is perfect.
PeriodicityOfIrregularEventsIsLowAndInputIsSorted	Fact	Periodicity of irregular events is low and input is sorted.
DispersionIndexMatchesClosedFormChiSquareTwoDegreesOfFreedom	Fact	Dispersion index matches closed form chi square two degrees of freedom.
DispersionOfBurstyAndConstantCountsAndValidation	Fact	Dispersion of bursty and constant counts and validation.
DifferencingSquaresGivesOddNumbersAndSecondDifferencesAreConstantTwo	Fact	Differencing squares gives odd numbers and second differences are constant two.
DifferencingPropagatesNaNAndRejectsBadArguments	Fact	Differencing propagates na n and rejects bad arguments.
LagAndLeadShiftValuesAndPadWithNaN	Fact	Lag and lead shift values and pad with na n.
LaggedFeatureMatrixBuildsHandComputedRows	Fact	Lagged feature matrix builds hand computed rows.
LaggedFeatureMatrixValidatesLags	Fact	Lagged feature matrix validates lags.
CumulativeOperationsMatchHandComputation	Fact	Cumulative operations match hand computation.
CumulativeSumPropagatesNaNWhileMaximumIgnoresIt	Fact	Cumulative sum propagates na n while maximum ignores it.
PercentChangeMatchesHandComputationAndZeroBaselineIsNaN	Fact	Percent change matches hand computation and zero baseline is na n.
LogReturnOfExponentialGrowthIsConstantOne	Fact	Log return of exponential growth is constant one.
SimpleMovingAverageTrailingCenteredAndPartial	Fact	Simple moving average trailing centered and partial.
SimpleMovingAverageSkipsMissingAndRejectsBadWindow	Fact	Simple moving average skips missing and rejects bad window.
WeightedMovingAverageUsesOldestToNewestWeights	Fact	Weighted moving average uses oldest to newest weights.
ExponentialMovingAverageRecursiveAndAdjustedFormsMatchHandComputation	Fact	Exponential moving average recursive and adjusted forms match hand computation.
ExponentialMovingAverageRejectsAmbiguousParameters	Fact	Exponential moving average rejects ambiguous parameters.
ExponentialMovingStatisticsMatchHandComputedRecursion	Fact	Exponential moving statistics match hand computed recursion.
ExponentialMovingStatisticsOfConstantHasZeroSpread	Fact	Exponential moving statistics of constant has zero spread.
RollingStatisticsOverWindowOfThreeMatchHandComputation	Fact	Rolling statistics over window of three match hand computation.
RollingStatisticsIgnoreMissingAndCountFiniteValues	Fact	Rolling statistics ignore missing and count finite values.
ExpandingStatisticsMatchHandComputation	Fact	Expanding statistics match hand computation.
ExpandingStatisticsHandleMissingAndMinPeriods	Fact	Expanding statistics handle missing and min periods.
RollingCorrelationOfProportionalAndOppositeSeriesIsPlusAndMinusOne	Fact	Rolling correlation of proportional and opposite series is plus and minus one.
RollingCorrelationConstantWindowIsNaNAndMismatchRejected	Fact	Rolling correlation constant window is na n and mismatch rejected.
RollingZScoreOfSpikeUsesPrecedingWindowOnly	Fact	Rolling z score of spike uses preceding window only.
RollingZScoreConstantBaselineIsNaNAndIncludeCurrentChangesResult	Fact	Rolling z score constant baseline is na n and include current changes result.
DetrendLinearSeriesRecoversInterceptAndSlope	Fact	Detrend linear series recovers intercept and slope.
DetrendMeanAndPolynomialMatchClosedForms	Fact	Detrend mean and polynomial match closed forms.
FillLinearInterpolationForwardBackwardNearestAndConstant	Fact	Fill linear interpolation forward backward nearest and constant.
FillEdgeGapsAndAllMissing	Fact	Fill edge gaps and all missing.
MedianFilterRemovesSpikesAndReplicatesEdges	Fact	Median filter removes spikes and replicates edges.
MedianFilterRejectsEvenWindowAndKeepsConstant	Fact	Median filter rejects even window and keeps constant.
HampelFlagsSingleSpikeAndReplacesWithLocalMedian	Fact	Hampel flags single spike and replaces with local median.
HampelLeavesCleanSeriesAlone	Fact	Hampel leaves clean series alone.
SavitzkyGolayWindowFiveOrderTwoUsesTextbookCoefficients	Fact	Savitzky golay window five order two uses textbook coefficients.
SavitzkyGolayReproducesPolynomialAndItsDerivativesIncludingEdges	Fact	Savitzky golay reproduces polynomial and its derivatives including edges.
SavitzkyGolayValidatesParameters	Fact	Savitzky golay validates parameters.
BoxCoxWithGivenLambdaMatchesDefinition	Fact	Box cox with given lambda matches definition.
BoxCoxEstimatesLambdaNearZeroForLogNormalQuantilesAndRejectsNonPositive	Fact	Box cox estimates lambda near zero for log normal quantiles and rejects non positive.
KalmanWithZeroProcessNoiseIsTheRunningMeanWithHandComputedVariances	Fact	Kalman with zero process noise is the running mean with hand computed variances.
KalmanSteadyStateGainForUnitSignalToNoiseIsTheInverseGoldenRatio	Fact	Kalman steady state gain for unit signal to noise is the inverse golden ratio.
SeriesProfileSummarisesMissingRunsAndMonotonicity	Fact	Series profile summarises missing runs and monotonicity.
SeriesProfileHandlesConstantAllMissingAndSeasonalSeries	Fact	Series profile handles constant all missing and seasonal series.

VariableTransformationApplierEdgeCaseTests

Jube.Test.AdvancedAnalytics.Statistics.VariableTransformationApplierEdgeCaseTests — 24 tests. Category: Unit.

Test	Kind	Verifies
AZeroScaleNeverDividesByZeroAndReturnsZeroInstead	Theory	A zero scale never divides by zero and returns zero instead.
ANonFiniteScaleNeverThrowsAndReturnsZeroInstead	Theory	A non finite scale never throws and returns zero instead.
LogOfZeroIsNaNNotAnException	Fact	Log of zero is na n not an exception.
LogOfANegativeValueIsNaNNotAnException	Fact	Log of a negative value is na n not an exception.
SqrtOfANegativeValueIsNaNNotAnException	Fact	Sqrt of a negative value is na n not an exception.
ReciprocalOfZeroIsNaNNotAnException	Fact	Reciprocal of zero is na n not an exception.
SquareAndAbsoluteValueAreAlwaysDefinedForNegativeInputs	Fact	Square and absolute value are always defined for negative inputs.
SignedLog1PIsDefinedForEveryRealValueIncludingNegatives	Theory	Signed log1 p is defined for every real value including negatives.
SignedSqrtIsDefinedForEveryRealValueIncludingNegatives	Theory	Signed sqrt is defined for every real value including negatives.
CubeRootIsDefinedForNegativeValuesUnlikeSquareRoot	Fact	Cube root is defined for negative values unlike square root.
MalformedParametersJsonForAScalingKindNeverThrowsAndFallsBackToTheRawValue	Theory	Malformed parameters json for a scaling kind never throws and falls back to the raw value.
UnparsableParametersJsonForADiscretisationKindNeverThrowsAndBehavesAsNoEdges	Theory	Unparsable parameters json for a discretisation kind never throws and behaves as no edges.
StructurallyValidButWrongTypedEdgesNeverThrowsAndFallsBackToTheRawValue	Theory	Structurally valid but wrong typed edges never throws and falls back to the raw value.
MalformedParametersJsonForACategoricalKindNeverThrowsAndFallsBackToZero	Theory	Malformed parameters json for a categorical kind never throws and falls back to zero.
MalformedParametersJsonForAOneHotSlotNeverThrowsAndFallsBackToZero	Fact	Malformed parameters json for a one hot slot never throws and falls back to zero.
AnUnseenCategoryNeverThrowsForAnyCategoricalTransformationKind	Theory	An unseen category never throws for any categorical transformation kind.
LabelOrdinalOfAnUnseenCategoryReturnsTheUnknownCode	Fact	Label ordinal of an unseen category returns the unknown code.
OneHotIndicatorOfAnUnseenCategoryReturnsZero	Fact	One hot indicator of an unseen category returns zero.
TargetMeanOfAnUnseenCategoryReturnsTheDefaultValue	Fact	Target mean of an unseen category returns the default value.
WeightOfEvidenceOfAnUnseenCategoryReturnsTheDefaultValue	Fact	Weight of evidence of an unseen category returns the default value.
FrequencyOfAnUnseenCategoryReturnsTheDefaultValue	Fact	Frequency of an unseen category returns the default value.
CallingApplyNumericWithACategoricalKindThrowsALoudProgrammingError	Fact	Calling apply numeric with a categorical kind throws a loud programming error.
CallingApplyCategoricalWithANumericKindThrowsALoudProgrammingError	Fact	Calling apply categorical with a numeric kind throws a loud programming error.
TheApplierIsPureAndSafeUnderConcurrentUseAcrossManyThreads	Fact	The applier is pure and safe under concurrent use across many threads.

VariableTransformationApplierTests

Jube.Test.AdvancedAnalytics.Statistics.VariableTransformationApplierTests — 19 tests. Category: Unit.

Test	Kind	Verifies
ColumnFunctionsMatchScalingToolsApplyColumnFunction	Theory	Column functions match scaling tools apply column function.
BoxCoxMatchesScalingToolsApplyPowerTransformer	Fact	Box cox matches scaling tools apply power transformer.
YeoJohnsonMatchesScalingToolsApplyPowerTransformer	Fact	Yeo johnson matches scaling tools apply power transformer.
TableScalingMatchesScalingToolsApplyTableScaler	Theory	Table scaling matches scaling tools apply table scaler.
QuantileTransformMatchesScalingToolsApplyQuantileTransformer	Theory	Quantile transform matches scaling tools apply quantile transformer.
WinsoriseMatchesScalingToolsApplyOutlierClipper	Fact	Winsorise matches scaling tools apply outlier clipper.
DiscretisationMatchesBinningToolsApplyBinEdges	Theory	Discretisation matches binning tools apply bin edges.
DiscretiseSupervisedMatchesBinningToolsApplyBinEdges	Fact	Discretise supervised matches binning tools apply bin edges.
DiscretisationOfAMissingValueReturnsMinusOne	Fact	Discretisation of a missing value returns minus one.
CyclicalSinAndCosMatchFeatureEngineeringToolsEncodeCyclicalFeature	Fact	Cyclical sin and cos match feature engineering tools encode cyclical feature.
LabelOrdinalMatchesEncodingToolsApplyLabelEncoder	Fact	Label ordinal matches encoding tools apply label encoder.
LabelOrdinalOfAnUnseenCategoryMatchesTheUnknownCode	Fact	Label ordinal of an unseen category matches the unknown code.
OneHotIndicatorMatchesEncodingToolsApplyOneHotEncoderForOneSelectedCategory	Fact	One hot indicator matches encoding tools apply one hot encoder for one selected category.
TargetMeanMatchesEncodingToolsApplyCategoryEncoder	Fact	Target mean matches encoding tools apply category encoder.
WeightOfEvidenceMatchesEncodingToolsApplyCategoryEncoder	Fact	Weight of evidence matches encoding tools apply category encoder.
FrequencyMatchesEncodingToolsApplyCategoryEncoder	Fact	Frequency matches encoding tools apply category encoder.
ACategoricalTransformationOfAnUnseenCategoryFallsBackToTheDefaultValue	Fact	A categorical transformation of an unseen category falls back to the default value.
NoneReturnsTheRawValueUnchanged	Fact	None returns the raw value unchanged.
EveryNumericTransformationOfAMissingValueIsNaNExceptDiscretisationWhichIsMinusOne	Fact	Every numeric transformation of a missing value is na n except discretisation which is minus one.