Informatics and Applications
2018, Volume 12, Issue 4, pp 75-85
NEW MIXTURE REPRESENTATIONS OF THE GENERALIZED MITTAG-LEFFLER DISTRIBUTION AND THEIR APPLICATIONS
- V. Yu. Korolev
- A. K. Gorshenin
- A. I. Zeifman
Abstract
The article provides new mixture represenations for the generalized Mittag-Leffler distribution. In particular, it is shown that for values of the "generalizing" parameter not exceeding one, the generalized Mittag- Leffler distribution is a scale mixture of the half-normal distribution laws, classic Mittag-Leffler distributions, or generalized Mittag-Leffler distributions with the larger values of the characteristic index. The explicit expressions for mixing quantities are given for all cases. The obtained representations allow proposing new algorithms for modeling random variables with the generalized Mittag-Leffler distribution and formulating new limit theorems in which such distributions appear as the limit ones.
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[+] About this article
Title
NEW MIXTURE REPRESENTATIONS OF THE GENERALIZED MITTAG-LEFFLER DISTRIBUTION AND THEIR APPLICATIONS
Journal
Informatics and Applications
2018, Volume 12, Issue 4, pp 75-85
Cover Date
2018-12-30
DOI
10.14357/19922264180411
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
generalized Mittag-Leffler distribution; scale mixture; generalized gamma distribution; half-normal distribution; stable distribution
Authors
V. Yu. Korolev , , ,
A. K. Gorshenin , ,
and A. I. Zeifman , ,
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Hangzhou Dianzi University, Xiasha Higher Education Zone, Hangzhou 310018, China
Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Vologda Research Center of the Russian Academy of Sciences, 56-A Gorky Str., Vologda 160001, Russian Federation
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