On Ordered Beta Distribution and the Generalized Incomplete Beta Function

Mayad Al-Saidi (), Alexey Kuznetsov () and Mikhail Nediak ()
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Mayad Al-Saidi: York University
Alexey Kuznetsov: York University
Mikhail Nediak: Queen’s University

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 1, 1-16

Abstract: 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.

Keywords: Beta distribution; Beta function; Incomplete beta function; Ordered simplex; Chebyshev polynomials; Primary 60E05; Secondary 65D15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-024-10129-3

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