Showing papers on "Multivariate gamma function published in 1982"
TL;DR: In this article, a Monte Carlo study of approximating the non-central Wishart distribution by Central Wishart distributions by multivariate Gram-Chalier expansion and 2.2 Laguerre polynomial expansion is presented.
Abstract: This paper provides a Monte Carlo study of approximating the non-central Wishart distribution by Central Wishart distribution by mean of 1. Multivariate Gram-Chalier expansion and 2. Laguerre polynomial expansion. For assessing the closeness of these approximations, 1,000 independent 2×2 non-central Wishart matrices are generated by computer. The numerical results indicate that the multivariate Gram-Chalier expansion provides a close approximation to the non-central Wishart distribution as long as the correlation coefficient is less than 0.8. Also, it appears that the Gram-Chalier expansion approximation is better than the Laguerre polynomial expansion approximation when the probability values are large.
11 citations
1 Jan 1982
TL;DR: In this paper, the problems of evaluating PreS > n, when S has a Wishart or multivariate beta distribution and n is a given positive definite matrix, were studied, and the most general results were obtained for the central distributions, while special cases were evaluated for the non-central distributions.
Abstract: We consider the problems of evaluating PreS > n), when S has a Wishart or multivariate beta distribution and n is a given positive definite matrix. The most general results are obtained for the central distributions, while special cases are evaluated for the non-central distributions. These results are applied to obtain the distributions of !. , the smallest latent root of S. We also evaluate special cases of mln Pr(n < S < 1\.) for the central distributions and thence derive expressions for the probability that all the latent roots of S lie in a given interval.
6 citations
2 citations