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Remarks on a Free Analogue of the Beta Prime Distribution

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  • Hiroaki Yoshida

    (Ochanomizu University)

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.

Suggested Citation

  • Hiroaki Yoshida, 2020. "Remarks on a Free Analogue of the Beta Prime Distribution," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1363-1400, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00924-x
    DOI: 10.1007/s10959-019-00924-x
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    References listed on IDEAS

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    1. Bryc, Wlodek, 2010. "Markov processes with free-Meixner laws," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1393-1403, August.
    2. Wiktor Ejsmont, 2014. "Characterizations of Some Free Random Variables by Properties of Conditional Moments of Third Degree Polynomials," Journal of Theoretical Probability, Springer, vol. 27(3), pages 915-931, September.
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