Pareto Distribution Definition - Statistics How To

The Pareto distribution is a skewed distribution with heavy, or “slowly decaying” tails (i.e. much of the data is in the tails). ShareonProbabilityDistributions> WhatistheParetoDistribution? TheParetodistributionisaskeweddistributionwithheavy,or“slowlydecaying”tails(i.e.muchofthedataisinthetails). TheParetodistribution.Image:Danvildanvil|wikimediacommons TheParetodistribution(createdbythe19thCenturyItalianeconomistVilfredoPareto)isdefinedbyashapeparameter,α(alsocalledaslopeparameterorParetoIndex)andalocationparameter,X.Ithastwomainapplications: Tomodelthedistributionofincomes. Tomodelthedistributionofcitypopulations. However,itcanbeusedinavarietyofothersituations.Forexample,itcanbeusedtomodelthelifetimeofamanufactureditemwithacertainwarrantyperiod. TheParetodistributionisexpressedas: F(x)=1–(k/x)α where xistherandomvariable kisthelowerboundofthedata αistheshapeparameter Youmightalsoseethiswrittenas: F(x)=1–(kλk/xk+1)α Whenusedtomodelincomedistribution,thisparticularversionoftheformulahasλastheminimumincomeandkasthedistributionofincome. TheSurvivalFunction MosttextsontheParetofunctionmentiona“survivalfunction,”althoughthisissometimesalsocalledatailfunctionorreliabilityfunction.ThisisjusttheprobabilityofvaluesgreaterthanX.Forexample,youmaybelookingathouseholdincomeintheUnitedStatesandwanttoknowwhatproportionofhouseholdincomeisgreaterthan$1,000,000. TheParetoPrinciple TheParetoPrincipleisderivedfromtheParetodistributionandisusedtoillustratethatmanythingsarenotdistributedevenly.Originallywrittentostatethat20%ofthepopulationholds80%ofthewealth,itcanbeappliedmoreuniversally.Forexample,1%ofthepopulationholds99%ofthewealth.However,itcanbeusedtomodelanygeneralsituationwheresituationsarenotevenlydistributed.Forexample,thetop20%ofworkersmightproduce80%ofoutput. Next:TheParetoPrinciple. CITETHISAS:StephanieGlen."ParetoDistributionDefinition"FromStatisticsHowTo.com:ElementaryStatisticsfortherestofus!https://www.statisticshowto.com/pareto-distribution/ --------------------------------------------------------------------------- Needhelpwithahomeworkortestquestion?WithCheggStudy,youcangetstep-by-stepsolutionstoyourquestionsfromanexpertinthefield.Yourfirst30minuteswithaCheggtutorisfree! Comments?Needtopostacorrection?PleasepostacommentonourFacebookpage. StatisticsHowToFacebookPage ByStephanie| May6,2015| StatisticsHowTo| ←ParetoPrinciple(The80/20Rule)&ParetoAnalysis ExtraneousVariableSimpleDefinition→ Search NEEDHELPwithahomeworkproblem?CLICKHERE!Needhelpwithahomeworkortestquestion?WithCheggStudy,youcangetstep-by-stepsolutionstoyourquestionsfromanexpertinthefield.Yourfirst30minuteswithaCheggtutorisfree! Feellike“cheating”atStatistics?CheckoutourPracticallyCheatingStatisticsHandbook,whichgivesyouhundredsofeasy-to-followanswersinaPDFformat.Recommendedreadingattopuniversities! NEEDHELPwithahomeworkproblem?CLICKHERE! Latestarticles Clopper-PearsonExactMethod MeanAbsolutePercentageError(MAPE) DataGranularity Chi-Bar-SquaredDistribution FuzzyClustering:Definition CrampFunctionDistribution BernoulliTrials:Definition,Examples ANCOVA:AnalysisofCovariance NEEDHELPwithahomeworkproblem?CLICKHERE!