Integral representations for convolutions of non-central multivariate gamma distributions

Details Integral representations for convolutions of non-central multivariate gamma distributions Integral representations for convolutions of non-central multivariate gamma distributions

2007-04-04

arxiv.org/abs/0704.0539v1

Mathematics

Statistics Theory

12 pages

Scientific paper

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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