Generalized Pareto Distribution | Pareto distribution
Definition. The probability density function for the generalized Pareto distribution with shape parameter k ≠ 0, scale parameter σ, and threshold parameter θ, is.SkiptocontentDocumentationHelpCenterDocumentationSearchSupportSupportMathWorksSearchMathWorks.comMathWorksSupportCloseMobileSearchOpenMobileSearchOff-CanvasNavigationMenuToggleDocumentationHomeStatisticsandMachineLearningToolboxProbabilityDistributionsContinuousDistributionsGeneralizedParetoDistributionGeneralizedParetoDistributionOnthispageDefinitionBackgroundParametersExamplesComputeGeneralizedParetoDistributionpdfReferencesSeeAlsoRelatedTopicsDocumentationAllExamplesFunctionsBlocksAppsVideosAnswersTrialSoftwareTrialSoftwareProductUpdatesProductUpdatesResourcesDocumentationAllExamplesFunctionsBlocksAppsVideosAnswersMainContentGeneralizedParetoDistributionDefinitionTheprobabilitydensityfunctionforthegeneralizedParetodistributionwithshapeparameterk≠0,scaleparameterσ,andthresholdparameterθ,isy = f(x|k,σ,θ)= (1σ)(1+k(x−θ)σ)−1−1kforθ0,orforθ0andθ=σ/k,thegeneralizedParetodistributionisequivalenttotheParetodistributionwithascaleparameterequaltoσ/kandashapeparameterequalto1/k.BackgroundLiketheexponentialdistribution,thegeneralizedParetodistributionisoftenusedtomodelthetailsofanotherdistribution.Forexample,youmighthavewashersfromamanufacturingprocess.Ifrandominfluencesintheprocessleadtodifferencesinthesizesofthewashers,astandardprobabilitydistribution,suchasthenormal,couldbeusedtomodelthosesizes.However,whilethenormaldistributionmightbeagoodmodelnearitsmode,itmightnotbeagoodfittorealdatainthetailsandamorecomplexmodelmightbeneededtodescribethefullrangeofthedata.Ontheotherhand,onlyrecordingthesizesofwasherslarger(orsmaller)thanacertainthresholdmeansyoucanfitaseparatemodeltothosetaildata,whichareknownasexceedances.Youcanusethegener
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