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- Title
Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables.
- Authors
Koyama, Tamio; Takemura, Akimichi
- 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.
- Subjects
HOLONOMIC constraints; NONHOLONOMIC constraints; CONSTRAINTS (Physics); CHI-square distribution; DISTRIBUTION (Probability theory)
- Publication
Computational Statistics, 2016, Vol 31, Issue 4, p1645
- ISSN
0943-4062
- Publication type
Article
- DOI
10.1007/s00180-015-0625-3