Systems and Means of Informatics
2021, Volume 31, Issue 2, pp 108-118
ANALYTICAL PROPERTIES AND ASPECTS OF COMPUTATION OF THE GAMMA-EXPONENTIAL FUNCTION
- M. O. Vorontsov
- A. A. Kudryavtsev
- S. Ya. Shorgin
Abstract
Mixtures of probability distributions play an important role in modern analysis and modeling of complex processes. Traditionally, much research attention is paid to the distributions from the gamma class. The main probabilistic characteristics of scale mixtures of generalized gamma distributions cannot be expressed in elementary functions that complicates the process of analytical research and often leads to unreasonably large computational difficulties. The paper analyzes aspects of computation and analytical properties of the gamma- exponential function which has proven itself as a convenient tool for studying scale mixtures of generalized gamma distributions. The presented results expand the usage of functions like the Mittag-Leffler function in the analysis of probability distributions.
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[+] About this article
Title
ANALYTICAL PROPERTIES AND ASPECTS OF COMPUTATION OF THE GAMMA-EXPONENTIAL FUNCTION
Journal
Systems and Means of Informatics
Volume 31, Issue 2, pp 108-118
Cover Date
2021-05-20
DOI
10.14357/08696527210210
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
gamma-exponential function; generalized gamma distribution; scale mixture; computational algorithms
Authors
M. O. Vorontsov  , A. A. Kudryavtsev , and S. Ya. Shorgin 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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