English

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}
}
R2 v1 2026-06-22T08:41:17.820Z