Informatics and Applications
2019, Volume 13, Issue 4, pp 76-80
ON THE REPRESENTATION OF GAMMA-EXPONENTIAL AND GENERALIZED NEGATIVE BINOMIAL DISTRIBUTIONS
Abstract
For more than a century and a half, gamma-type distributions have shown their adequacy in modeling real processes and phenomena. Over time, designs using distributions from the gamma family are becoming more complex in order to improve the applicability of mathematical models to relevant aspects of life. The paper presents a number of results both generalizing and simplifying some classical forms used in the analysis of large-scale and structural mixtures of generalized gamma laws. The gamma-exponential distribution is introduced and its characteristics are described. An explicit form for integral representations of partial probabilities of the generalized negative binomial distribution is given. The results are formulated in terms of the gamma exponential function. The obtained results can be widely used in models that use scale and structural mixtures of distributions with positive unrestricted support to describe processes and phenomena.
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[+] About this article
Title
ON THE REPRESENTATION OF GAMMA-EXPONENTIAL AND GENERALIZED NEGATIVE BINOMIAL DISTRIBUTIONS
Journal
Informatics and Applications
2019, Volume 13, Issue 4, pp 76-80
Cover Date
2019-12-30
DOI
10.14357/19922264190412
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
gamma exponential function; generalized gamma distribution; generalized negative binomial distribution; gamma-exponential distribution; mixed distributions
Authors
A. A. Kudryavtsev 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
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