Resumen de Muliere and Scarsini's bivariate Pareto distribution: sums, products, and ratios.

Samuel Kotz, Saralees Nadarajah

• HolaWe derive the exact distributions of R = X +Y , P = X Y andW = X/(X +Y ) and the corresponding moment properties when X and Y follow Muliere and Scarsini¿s bivariate Pareto distribution. The expressions turn out to involve special functions.

  We also provide extensive tabulations of the percentage points associated with the distributions.

  These tables ¿obtained using intensive computing power¿ will be of use to practitioners of the bivariate Pareto distribution.

  MSC: 33C90, 62E99 Keywords: incomplete beta function, Gauss hypergeometric function, Muliere and Scarsini¿s bivariate Pareto distribution, products of random variables, ratios of random variables, sums of random variables HolaTrobem la distribuci¿o exacta de R = X + Y , P = X Y, W = X/(X + Y ), els corresponents moments i les seves propietats quan X, Y segueixen la distribuci¿o bivariant Pareto de Muliere i Scarsini. Les expressions fan servir funcions especials.

  Tamb¿e proporcionem tabulacions extensives dels percentils associats amb les distribucions.

  Aquestes taules ¿obtingudes emprant potents t`ecniques de computaci¿o intensiva¿ seran d¿utilitat per als usuaris de la distribuci¿o de Pareto bivariant.

  Paraules clau: funci¿o beta incompleta, funci¿o hypergeom`etrica de Gauss, distribuci ¿o bivariant Pareto de Muliere i Scarsini, productes de variables aleat`ories, quocients de variables aleat`ories, sumes de variables aleat`ories