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

Author

Listed:
  • Kume, Alfred
  • Sei, Tomonari
  • Wood, Andrew T.A.

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.

Suggested Citation

  • Kume, Alfred & Sei, Tomonari & Wood, Andrew T.A., 2025. "On the representation and computational aspects of the distribution of a linear combination of independent noncentral chi-squared random variables," Statistics & Probability Letters, Elsevier, vol. 218(C).
    • Handle: RePEc:eee:stapro:v:218:y:2025:i:c:s0167715224002608
    DOI: 10.1016/j.spl.2024.110291
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