Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables
Statistics Theory
2015-09-01 v3 Statistics Theory
Abstract
We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution.
Keywords
Cite
@article{arxiv.1503.00378,
title = {Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables},
author = {Tamio Koyama and Akimichi Takemura},
journal= {arXiv preprint arXiv:1503.00378},
year = {2015}
}