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On Ordered Beta Distribution and the Generalized Incomplete Beta Function

Author

Listed:
  • Mayad Al-Saidi

    (York University)

  • Alexey Kuznetsov

    (York University)

  • Mikhail Nediak

    (Queen’s University)

Abstract

Motivated by applications in Bayesian analysis, we introduce a multidimensional beta distribution in the ordered simplex. We study the properties of this distribution and connect them with the generalized incomplete beta function. This function is crucial in applications of multidimensional beta distribution. Thus, we present two efficient numerical algorithms for computing the generalized incomplete beta function, one based on Taylor series expansion and another based on Chebyshev polynomials.

Suggested Citation

  • Mayad Al-Saidi & Alexey Kuznetsov & Mikhail Nediak, 2025. "On Ordered Beta Distribution and the Generalized Incomplete Beta Function," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-16, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-024-10129-3
    DOI: 10.1007/s11009-024-10129-3
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