Pareto Distribution -- from Wolfram MathWorld

The distribution with probability density function and distribution function P(x) = (ab^a)/(x^(a+1)) (1) D(x) = 1-(b/x)^a (2) defined over the interval x>=b ... Algebra AppliedMathematics CalculusandAnalysis DiscreteMathematics FoundationsofMathematics Geometry HistoryandTerminology NumberTheory ProbabilityandStatistics RecreationalMathematics Topology AlphabeticalIndex NewinMathWorld ProbabilityandStatistics StatisticalDistributions ContinuousDistributions HistoryandTerminology WolframLanguageCommands ParetoDistribution Download Wolfram Notebook Thedistributionwithprobabilitydensityfunctionanddistributionfunction (1) (2) definedovertheinterval. ItisimplementedintheWolframLanguageasParetoDistribution[k, alpha]. Thethrawmomentis (3) for,givingthefirstfewas (4) (5) (6) (7) Thethcentral momentis (8) (9) forandwhereisagammafunction, isaregularizedhypergeometric function,andisabeta function,givingthefirstfewas (10) (11) (12) Themean,variance,skewness, andkurtosisexcessaretherefore (13) (14) (15) (16) ExplorewithWolfram|Alpha Morethingstotry: paretodistribution (1-1/3+1/5)/(1/2-1/4+1/6) FTsinct ReferencesvonSeggern,D.CRCStandardCurvesandSurfaces.BocaRaton,FL:CRCPress,p. 252,1993.Referenced onWolfram|AlphaParetoDistribution Citethisas: Weisstein,EricW."ParetoDistribution." FromMathWorld--AWolframWebResource.https://mathworld.wolfram.com/ParetoDistribution.html Subjectclassifications ProbabilityandStatistics StatisticalDistributions ContinuousDistributions HistoryandTerminology WolframLanguageCommands Created,developedandnurturedbyEricWeissteinatWolframResearch