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

Author

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  • Tamio Koyama

    (University of Tokyo
    Japan Society for the Promotion of Science)

  • Akimichi Takemura

    (University of Tokyo)

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.

Suggested Citation

  • Tamio Koyama & Akimichi Takemura, 2016. "Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables," Computational Statistics, Springer, vol. 31(4), pages 1645-1659, December.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-015-0625-3
    DOI: 10.1007/s00180-015-0625-3
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    References listed on IDEAS

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    1. A. Kume & Andrew T. A. Wood, 2005. "Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants," Biometrika, Biometrika Trust, vol. 92(2), pages 465-476, June.
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    Cited by:

    1. Kuriki, Satoshi & Takemura, Akimichi & Taylor, Jonathan E., 2022. "The volume-of-tube method for Gaussian random fields with inhomogeneous variance," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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