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Estimates of the Convergence Rate in the Generalized Rényi Theorem with a Structural Digamma Distribution Using Zeta Metrics

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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
    Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow 119333, Russia)

Abstract

This paper considers a generalization of the Rényi theorem to the case of a structural distribution with a scale parameter. In terms of the zeta metric, some estimates of the convergence rate in the generalized Rényi theorem are obtained when the structural mixed Poisson distribution of the summation index is a scale mixture of the generalized gamma distribution. Estimates of the convergence rate for the structural digamma distribution are given as a special case. The paper extends the results previously obtained for the generalized gamma distribution.

Suggested Citation

  • Alexey Kudryavtsev & Oleg Shestakov, 2023. "Estimates of the Convergence Rate in the Generalized Rényi Theorem with a Structural Digamma Distribution Using Zeta Metrics," Mathematics, MDPI, vol. 11(21), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4477-:d:1269767
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    References listed on IDEAS

    as
    1. Chen, Wangxue & Xie, Minyu & Wu, Ming, 2013. "Parametric estimation for the scale parameter for scale distributions using moving extremes ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2060-2066.
    2. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    3. 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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