Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables

2015/03/01 by Koyama, Tamio, Takemura, Akimichi
#16S32 #32C38 #62H10 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1503.00378

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.

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