NON-CENTRAL MULTIVARIATE CHI-SQUARE AND GAMMA DISTRIBUTIONS
A -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 To facilitate the computation, these formulas are given more detailed for These -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” -correlation matrix R, i.e., Rdiffers from a suitable diagonal matrix only by a matrix of rank 1, which holds in particular for all -Rwith no vanishing correlation.
non-central multivariate chi-square distribution, non-central multivariate gamma distribution.