A Pareto2 (1/b, a) distribution describes the time between events where the number of random events occurring in a unit of time follows a Pólya (a,b) distribution.HomePelicanERMSoftwareWhatisPelican?Pelican-in-depthvideoWhatisEnterpriseRiskManagement?IsPelicanrightforyou?WhatmakesPelicanspecial?Videos,whitepapers,casestudiesRiskmodelingsoftwareModelRisk-RiskAnalysisinExcelTamara-ProjectRiskAnalysisPurchaseResourcesFrequentlyaskedquestionsExampleriskmodelsVideos,whitepapers,casestudiesTheVoseWikionriskMonteCarlosimulation-asimpleexplanationServicesRiskmanagementconsultingTrainingTechnicalsupportCustomSoftwareDevelopmentCompanyBlogOurhistoryOurclientsContactPurchaseParetodistributionofthesecondkindFormat:Pareto2(b,q) ThisdistributionissimplyastandardParetodistribution(ofthefirstkind)butshiftedalongthex-axissothatitstartsatx=0.Thisismostreadilyapparentbystudyingthecumulativedistributionfunctionsforthetwodistributions:Pareto: Pareto2:TheonlydifferencebetweenthetwoequationsisthatxfortheParetohasbeenreplacedby(x+b)forthePareto2.Inotherwords:VosePareto2(b,q)=VosePareto(q,a)-awherea=b,andq=qThusbothdistributionshavethesamevarianceandshapewhena=bandq=q,butdifferentmeans.UsesAPareto2(1/b,a)distributiondescribesthetimebetweeneventswherethenumberofrandomeventsoccurringinaunitoftimefollowsaPólya(a,b)distribution.Thisismorethananacademiccuriosity.ItiscommonlyassumedthateventsoccurringrandomlyintimefollowaPoissondistribution,fromwhichitcanbedeterminedthatthetimebetweeneventsfollowsanExponentialdistribution.However,manyeventsseemtoshowsomeclusteringintheirtiming,whichmeansthattherearemoreeventsclosertogetherandfurtherapartthantheExponentialdistributionwouldpredict.FittingthetimebetweeneventsusingbothaPareto2andanExponentialdistribution,thencomparingwhichdistributionfitsbetter,allowsonetoassesswhetheraPólyaoraPoissonshouldbeusedformodelingfrequency.Onemightargue-whynotjustfitthefrequencydatainthefirstplace?Theproblemwithfrequencydataisthatitisinformation-poor.Ifweknowwheneventsoccur