Remarks on a Free Analogue of the Beta Prime Distribution

Hiroaki Yoshida ()
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Hiroaki Yoshida: Ochanomizu University

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1363-1400

Abstract: Abstract We introduce the free analogue of the classical beta prime distribution by the multiplicative free convolution of the free Poisson and the reciprocal of free Poisson distributions, and related free analogues of the classical F, T, and beta distributions. We show the rationales of our free analogues via the score functions and the potentials. We calculate the moments of the free beta prime distribution explicitly in combinatorial fashion by using non-crossing linked partitions and demonstrate that the free beta prime distribution belongs to the class of the free negative binomials in the free Meixner family.

Keywords: Free beta prime distribution; Free F-distribution; Free T-distribution; Free beta distribution; Non-crossing linked partitions; Free Meixner family; 46L54; 60E05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00924-x

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