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

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12 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
pagine (da-a)563-575
Numero di pagine13
RivistaIntegral Transforms and Special Functions
Volume19
Stato di pubblicazionePublished - 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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