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arXiv · 1908.07887

Free self-decomposability and unimodality of the Fuss-Catalan distributions

Wojciech Młotkowski·Noriyoshi Sakuma·Yuki Ueda
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Abstract

We study properties of the Fuss-Catalan distributions $\mu(p,r)$, $p\geq1$, $0<r\leq p$: free infinite divisibility, free self-decomposability, free regularity and unimodality. We show that the Fuss-Catalan distribution $\mu(p,r)$ is freely self-decomposable if and only if $1 \leq p=r \leq 2$.

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Wojciech Młotkowski, Noriyoshi Sakuma, Yuki Ueda. 2019-08-21. Free self-decomposability and unimodality of the Fuss-Catalan distributions. https://doi.org/10.1007/s10955-020-02488-1

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