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arXiv · 1604.06906

Non-Central Multivariate Chi-Square and Gamma Distributions

Thomas Royen
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Abstract

A (p-1)-variate integral representation is given for the cumulative distribution function of the general p-variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known analytical functions is integrated over arguments from (-pi,pi). To facilitate the computation, these formulas are given more detailed for p=2 and p=3. These (p-1)-variate integrals are also derived for the diagonal of a non-central complex Wishart Matrix. Furthermore, some alternative formulas are given for the cases with an associated "one-factorial" (pxp)-correlation matrix R, i.e. R differs from a suitable diagonal matrix only by a matrix of rank 1, which holds in particular for all (3x3)-R with no vanishing correlation.

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Thomas Royen. 2016-04-23. Non-Central Multivariate Chi-Square and Gamma Distributions. https://arxiv.org/abs/1604.06906

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