Integral representations for convolutions of non-central multivariate gamma distributions

2007/04/04 by Thomas Royen, Royen, Thomas · 2 citations
Decision Sciences · Mathematics · #62E15 #62H10 #FOS: Mathematics #Mathematical functions and polynomials #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #msc:62E15 #msc:62H10 #stat.TH

paper · pdf · doi:10.48550/arxiv.0704.0539

12 pages

arxiv created 2007/04/04 · openalex publication_date 2007/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Three types of integral representations for the cumulative distribution functions of convolutions of non-central p-variate gamma distributions are given by integration of elementary complex functions over the p-cube Cp = (-pi,pi]x...x(-pi,pi]. In particular, the joint distribution of the diagonal elements of a generalized quadratic form XAX' with n independent normally distributed column vectors in X is obtained. For a single p-variate gamma distribution function (p-1)-variate integrals over Cp-1 are derived. The integrals are numerically more favourable than integrals obtained from the Fourier or laplace inversion formula.

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