Integral Representations and Approximations for Multivariate Gamma Distributions |
| |
Authors: | T Royen |
| |
Institution: | (1) Fachhochschule Bingen, University of Applied Sciences, Berlinstrasse 109, 55411 Bingen, Germany |
| |
Abstract: | Let 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
-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
-variate integral if p = 3 or p = 4. Since computation is only feasible for small m, a given R is approximated by an m-factorial R
0. The cdf belonging to R is approximated by the cdf associated with R
0 and some additional correction terms with the deviations between R and R
0. |
| |
Keywords: | Multivariate gamma distribution Multivariate chi-square distribution Multivariate Rayleigh-distribution Approximation for positive definite matrices m-factorial matrices |
本文献已被 SpringerLink 等数据库收录! |
|