Informatics and Applications
2023, Volume 17, Issue 3, pp 58-63
A METHOD FOR ESTIMATING PARAMETERS OF THE GAMMA-EXPONENTIAL DISTRIBUTION FROM A SAMPLE WITH WEAKLY DEPENDENT COMPONENTS
- A. A. Kudryavtsev
- O. V. Shestakov
Abstract
The article proves the asymptotic normality of the estimators for the gamma-exponential distribution parameters obtained using the modified method of moments in the case of a weak dependence of the sample components. For the estimators of the bent and scale parameters of the gamma-exponential distribution with fixed shape and concentration parameters, the central limit theorem is proved in the case when the maximum correlation coefficient between the sample elements tends to zero. The proof is based on the study of the sample spectral density and the results of the theory of stationary random sequences. The results of the article can be used to substantiate the asymptotic normality of the estimators for the parameters of the digamma distribution, the particular types of which include the generalized gamma distribution and the generalized beta distribution of the second kind that arise when describing processes modeled with distributions having a nonnegative unbounded support.
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[+] About this article
Title
A METHOD FOR ESTIMATING PARAMETERS OF THE GAMMA-EXPONENTIAL DISTRIBUTION FROM A SAMPLE WITH WEAKLY DEPENDENT COMPONENTS
Journal
Informatics and Applications
2023, Volume 17, Issue 3, pp 58-63
Cover Date
2023-10-10
DOI
10.14357/19922264230308
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
weak dependence; parameter estimation; gamma-exponential distribution; mixed distributions; method of moments; asymptotic normality
Authors
A. A. Kudryavtsev  ,  and O. V. Shestakov , , 
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
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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