Informatics and Applications
2026, Volume 20, Issue 2, pp 74-81
ASYMPTOTIC PROPERTIES OF DIGAMMA DISTRIBUTION PARAMETER ESTIMATES CONSTRUCTED FROM A SAMPLE WITH WEAKLY DEPENDENT COMPONENTS
- A. A. Kudryavtsev
- O. V. Shestakov
Abstract
The paper considers the digamma distribution, special cases of which can be represented as a generalized gamma distribution and a generalized beta distribution of the second kind. The strong consistency and asymptotic normality of digamma distribution parameter estimates obtained using a modified method of moments based on sample cumulants are proved in the case of weakly dependent sample components. Estimates of three unknown parameters (the characteristic exponent, shape parameters, and scale parameters) are considered for fixed concentration parameters. Estimation of the latter is not considered due to the nontrivial nature of the inversion of polygamma functions. The formulated statements pertain to a limited set of values of the estimated parameters; however, they can be easily extended to the general case using an estimation algorithm detailed in the authors' previous cited papers. The proof of the main statement is based on a sufficient condition for weak convergence of functions of asymptotically normal vectors. The results of this paper can be used to describe a wide class of distributions arising in the description of processes modeled by distributions with nonnegative, unbounded support.
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[+] About this article
Title
ASYMPTOTIC PROPERTIES OF DIGAMMA DISTRIBUTION PARAMETER ESTIMATES CONSTRUCTED FROM A SAMPLE WITH WEAKLY DEPENDENT COMPONENTS
Journal
Informatics and Applications
2026, Volume 20, Issue 2, pp 74-81
Cover Date
2026-10-07
DOI
10.14357/19922264260206
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
weak dependence; parameter estimation; digamma distribution; mixed distributions; method of moments; cumulants; 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 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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