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Matrix hypergeometric function and its application to computation of characteristic function of spherically symmetric distributions with phase-type amplitude

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  • Nałęcz, Marek

Abstract

The paper presents a new definition of a matrix-valued Gauss hypergeometric function 2F1 of a matrix argument. The proposed function is applied in the context of computing a characteristic function for spherically symmetric random vectors whose amplitude has phase-type distribution. It is proved that the characteristic function can be expressed as a specialized case of the Gauss hypergeometric function with the argument related to a matrix representation of the phase-type distribution. Then it is shown that this specialized case of the 2F1 function can be evaluated by using closed-form formulas, which involve only elementary functions and thus can reliably be computed numerically for a matrix argument. Explicit formulas are derived for the moments of the spherically symmetric distribution under consideration. As a by-product of the research, an erratum to the tables of special functions is proposed.

Suggested Citation

  • Nałęcz, Marek, 2021. "Matrix hypergeometric function and its application to computation of characteristic function of spherically symmetric distributions with phase-type amplitude," Statistics & Probability Letters, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:stapro:v:173:y:2021:i:c:s0167715221000249
    DOI: 10.1016/j.spl.2021.109062
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