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On Free Generalized Inverse Gaussian Distributions
Title: | On Free Generalized Inverse Gaussian Distributions |
Authors: | Hasebe, Takahiro Browse this author →KAKEN DB | Szpojankowski, Kamil Browse this author |
Issue Date: | Oct-2019 |
Journal Title: | Complex Analysis and Operator Theory |
Volume: | 13 |
Issue: | 7 |
Start Page: | 3091 |
End Page: | 3116 |
Publisher DOI: | 10.1007/s11785-018-0790-9 |
Abstract: | 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. |
Rights: | 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. |
Type: | article |
URI: | http://hdl.handle.net/2115/75996 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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