On the representation and computational aspects of the distribution of a linear combination of independent noncentral chi-squared random variables

Alfred Kume, Tomonari Sei and Andrew T.A. Wood

Statistics & Probability Letters, 2025, vol. 218, issue C

Abstract: This article presents two new results relevant to a linear combination of χ2 random variables. The first result expresses the cumulative distribution function as a simple multiple of a certain tilted density. The second result shows that in important cases the inversion integral for the density may be expressed as a sum of relatively simple real integrals which, using suitable numerical methods, are straightforward to compute quickly and accurately.

Keywords: Bingham distribution; Fisher–Bingham distribution; Directional statistics; Holonomic function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110291

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