# Integral Representations and Approximations for Multivariate Gamma Distributions

@article{Royen2007IntegralRA, title={Integral Representations and Approximations for Multivariate Gamma Distributions}, author={Thomas Royen}, journal={Annals of the Institute of Statistical Mathematics}, year={2007}, volume={59}, pages={499-513} }

AbstractLet R be a p×p-correlation matrix with an “m-factorial” inverse R−1 = D − BB′ with diagonal D minimizing the rank m of B. A new
$$\left(m+1 \atop 2\right)$$-variate integral representation is given for p-variate gamma distributions belonging to R, which is based on the above decomposition of R−1 without the restriction D > 0 required in former formulas. This extends the applicability of formulas with small m. For example, every p-variate gamma cdf can be computed by an at most
$$\left(p…

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