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

Tamio Koyama and Akimichi Takemura ()
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Tamio Koyama: University of Tokyo
Akimichi Takemura: University of Tokyo

Computational Statistics, 2016, vol. 31, issue 4, No 21, 1645-1659

Abstract: 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: Algebraic statistics; Cumulative chi-square distribution; Fisher–Bingham distribution; Goodness of fit (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00180-015-0625-3

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