TY - JOUR

T1 - A characterization of the distribution of a weighted sum of Gamma variables through Multiple Hypergeometric functions.

AU - Di Salvo, Francesca

PY - 2008

Y1 - 2008

N2 - Applying the theory on multiple hypergeometric functions, the distribution of a weightedconvolution of Gamma variables is characterized through explicit forms for the probabilitydensity function, the distribution function and the moments about the origin.The main results unify some previous contributions in the literature on nite convolution ofGamma distributions.We deal with computational aspects that arise from the representations in terms of multiplehypergeometric functions, introducing a new integral representation for the fourth Lauricellafunction F(n)D and its conuent form (n)2 , suitable for numerical integration; some graphics ofthe probability density function and distribution function show that the proposed numericalapproach supply good estimates for the special functions involved. We briey outline twointeresting applications of Special function theory in Statistics: the weighted convolutions ofGamma matrices random variables and the weighted convolutions of Gamma variables withrandom weights.

AB - Applying the theory on multiple hypergeometric functions, the distribution of a weightedconvolution of Gamma variables is characterized through explicit forms for the probabilitydensity function, the distribution function and the moments about the origin.The main results unify some previous contributions in the literature on nite convolution ofGamma distributions.We deal with computational aspects that arise from the representations in terms of multiplehypergeometric functions, introducing a new integral representation for the fourth Lauricellafunction F(n)D and its conuent form (n)2 , suitable for numerical integration; some graphics ofthe probability density function and distribution function show that the proposed numericalapproach supply good estimates for the special functions involved. We briey outline twointeresting applications of Special function theory in Statistics: the weighted convolutions ofGamma matrices random variables and the weighted convolutions of Gamma variables withrandom weights.

KW - Dirichlet averages

KW - Lauricella functions

KW - Weighted Gamma Convolution

KW - con
uent hypergeometric
functions

KW - double Dirichlet averages

KW - multiple numerical integration.

KW - Dirichlet averages

KW - Lauricella functions

KW - Weighted Gamma Convolution

KW - con
uent hypergeometric
functions

KW - double Dirichlet averages

KW - multiple numerical integration.

UR - http://hdl.handle.net/10447/36728

M3 - Article

VL - 19

SP - 563

EP - 575

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

ER -