Integral Representations and Approximations for Multivariate Gamma Distributions

  title={Integral Representations and Approximations for Multivariate Gamma Distributions},
  author={Thomas Royen},
  journal={Annals of the Institute of Statistical Mathematics},
  • T. Royen
  • Published 11 September 2007
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
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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