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Asymptotically Normal Estimators for the Parameters of the Gamma-Exponential Distribution

Author

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  • Alexey Kudryavtsev

    (Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow 119991, Russia)

  • Oleg Shestakov

    (Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, Moscow 119991, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow 119991, Russia
    Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow 119333, Russia)

Abstract

Currently, much research attention has focused on generalizations of known mathematical objects in order to obtain adequate models describing real phenomena. An important role in the applied theory of probability and mathematical statistics is the gamma class of distributions, which has proven to be a convenient and effective tool for modeling many real processes. The gamma class is quite wide and includes distributions that have useful properties such as, for example, infinite divisibility and stability, which makes it possible to use distributions from this class as asymptotic approximations in various limit theorems. One of the most important tasks of applied statistics is to obtain estimates of the parameters of the model distribution from the available real data. In this paper, we consider the gamma-exponential distribution, which is a generalization of the distributions from the gamma class. Estimators for some parameters of this distribution are given, and the asymptotic normality of these estimators is proven. When obtaining the estimates, a modified method of moments was used, based on logarithmic moments calculated on the basis of the Mellin transform for the generalized gamma distribution. On the basis of the results obtained, asymptotic confidence intervals for the estimated parameters are constructed. The results of this work can be used in the study of probabilistic models based on continuous distributions with an unbounded non-negative support.

Suggested Citation

  • Alexey Kudryavtsev & Oleg Shestakov, 2021. "Asymptotically Normal Estimators for the Parameters of the Gamma-Exponential Distribution," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:273-:d:489838
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    References listed on IDEAS

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    1. Yi Zhou & Hongqing Zhu, 2018. "Image Segmentation Using a Trimmed Likelihood Estimator in the Asymmetric Mixture Model Based on Generalized Gamma and Gaussian Distributions," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-17, January.
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    Cited by:

    1. Alexey Kudryavtsev & Oleg Shestakov, 2023. "Limit Distributions for the Estimates of the Digamma Distribution Parameters Constructed from a Random Size Sample," Mathematics, MDPI, vol. 11(8), pages 1-13, April.

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