On Free Generalized Inverse Gaussian Distributions

Hasebe, Takahiro; Szpojankowski, Kamil

Complex Analysis and Operator Theory, 2019, 13(7), 3091-3116

Permalink : https://hdl.handle.net/2115/75996

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アクセス権	open access
URI	https://hdl.handle.net/2115/75996
タイトル	On Free Generalized Inverse Gaussian Distributions
著者	e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者	著者名 Szpojankowski, Kamil
言語	英語
発行日	2019-10
収録物名	Complex Analysis and Operator Theory
巻(号)	13(7)
ページ	3091-3116
抄録	We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and moreover we determine which distributions in this class are freely selfdecomposable. In the second part of the paper we prove that for free random variables X, Y where Y has a free Poisson distribution one has $X\triangleq\frac{1}{X+Y}$ if and only if X has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy.
資源タイプ	学術雑誌論文
出版タイプ	Version of Record
権利情報	This is a post-peer-review, pre-copyedit version of an article published in Complex analysis and operator theory. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11785-018-0790-9.
PISSN	1661-8254
EISSN	1661-8262
関連情報 (isIdenticalTo)	出版社版DOI https://doi.org/10.1007/s11785-018-0790-9