Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables
Tamio Koyama, Akimichi Takemura
TL;DR
This paper introduces a holonomic gradient method to efficiently compute the distribution function of a weighted sum of noncentral chi-square variables, which is crucial for multivariate normal analysis.
Contribution
The paper develops a novel application of the holonomic gradient method to the Fisher-Bingham distribution, enabling accurate computation of complex distribution functions.
Findings
Effective computation of the distribution function demonstrated.
Method outperforms traditional numerical approaches.
Applicable to multivariate normal and related distributions.
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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Taxonomy
TopicsMorphological variations and asymmetry · Bayesian Methods and Mixture Models · Advanced Statistical Methods and Models