On a Multivariate Analog of the Zolotarev Problem

Autor:	Yury Khokhlov, Victor Korolev
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	characterization problems multivariate geometric random sums multivariate anisotropic geometric stable distributions anisotropic multivariate Laplace distribution anisotropic multivariate Linnik distribution anisotropic multivariate Mittag–Leffler distribution Mathematics QA1-939
Zdroj:	Mathematics, Vol 9, Iss 15, p 1728 (2021)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math9151728
Popis:	A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) geometric stable distributions are extended to a more general case of “anisotropic” random summation where sums of independent random vectors with multivariate random index having a special multivariate geometric distribution are considered. Anisotropic-geometric stable distributions are introduced. It is demonstrated that these distributions are coordinate-wise scale mixtures of elliptically contoured stable distributions with the Marshall–Olkin mixing distributions. The corresponding “anisotropic” analogs of multivariate Laplace, Linnik and Mittag–Leffler distributions are introduced. Some relations between these distributions are presented.
Databáze:	Directory of Open Access Journals
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