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Teoriya Veroyatnostei i ee Primeneniya, 2016, Volume 61, Issue 4, Pages 753–773
DOI: https://doi.org/10.4213/tvp5086 (Mi tvp5086) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Limit distributions for doubly stochastically rarefied renewal processes and their properties

V. Yu. Korolevabc

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Hangzhou Dianzi University, Zhejiang
c Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
Full-text PDF (285 kB) Citations (11)
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DOI: https://doi.org/10.4213/tvp5086
Abstract: A limit theorem is proved for doubly stochastically rarefied renewal processes. It is shown that under rather general conditions, as limit laws in limit theorems for mixed geometric random sums, there appear mixed exponential and mixed Laplace distributions. Some known and new properties of these distributions are reviewed. Also, some nonobvious properties of special representatives of these classes (the Weibull, Mittag-Leffler, Linnik, and other distributions) are described.
Keywords: doubly stochastically rarefied renewal process, mixed geometric distribution, mixed geometric random sum, mixed exponential distribution, stable distribution, Weibull distribution, Mittag-Leffler distribution, Linnik distribution, Laplace distribution.
Funding agency Grant number
Russian Science Foundation 14-11-00364
Received: 05.10.2016
English version:
Theory of Probability and its Applications, 2017, Volume 61, Issue 4, Pages 649–664
DOI: https://doi.org/10.1137/S0040585X97T98840X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. Yu. Korolev, “Limit distributions for doubly stochastically rarefied renewal processes and their properties”, Teor. Veroyatnost. i Primenen., 61:4 (2016), 753–773; Theory Probab. Appl., 61:4 (2017), 649–664
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp5086
  • https://doi.org/10.4213/tvp5086
  • https://www.mathnet.ru/eng/tvp/v61/i4/p753
    • This publication is cited in the following 11 articles:
    1. V. Yu. Korolev, I. G. Shevtsova, O. V. Shestakov, “Asymptotic and Analytic Properties of Mixture Probability Models and Their Application to the Analysis of Complex Systems”, MoscowUniv.Comput.Math.Cybern., 48:4 (2024), 317  crossref
    2. Victor Korolev, “Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions”, Mathematics, 11:13 (2023), 2890  crossref
    3. Victor Korolev, Alexander Zeifman, “Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization”, Mathematics, 11:17 (2023), 3797  crossref
    4. V. Korolev, A. Gorshenin, “Probability models and statistical tests for extreme precipitation based on generalized negative binomial distributions”, Mathematics, 8:4 (2020), 604  crossref  isi
    5. V. Yu. Korolev, A. I. Zeifman, “Generalized negative binomial distributions as mixed geometric laws and related limit theorems”, Lith. Math. J., 59:3 (2019), 366–388  crossref  mathscinet  zmath  isi
    6. K. Gorska, A. Horzela, A. Lattanzi, “Composition law for the cole-cole relaxation and ensuing evolution equations”, Phys. Lett. A, 383:15 (2019), 1716–1721  crossref  mathscinet  isi  scopus
    7. V. Yu. Korolev, “Analogi teoremy Glezera dlya otritsatelnykh binomialnykh i obobschennykh gamma-raspredelenii i nekotorye ikh prilozheniya”, Inform. i ee primen., 11:3 (2017), 2–17  mathnet  crossref  elib
    8. V. Yu. Korolev, “Nekotorye svoistva raspredeleniya Mittag-Lefflera i svyazannykh s nim protsessov”, Inform. i ee primen., 11:4 (2017), 26–37  mathnet  crossref  elib
    9. V. Yu. Korolev, A. K. Gorshenin, “The probability distribution of extreme precipitation”, Dokl. Earth Sci., 477:2 (2017), 1461–1466  crossref  mathscinet  isi  scopus
    10. V. Korolev, A. Gorshenin, A. Korchagin, A. Zeifman, “Generalized gamma distributions as mixed exponential laws and related limit theorems”, Proceedings of the 31st European Conference on Modelling and Simulation (ECMS 2017), eds. Z. Paprika, P. Horak, K. Varadi, P. Zwierczyk, A. Vidovics-Dancs, J. Radics, European Council Modelling & Simulation, 2017, 642+ pp.  isi
    11. V.Yu. Korolev, A. K. Gorshenin, “O RASPREDELENII VEROYaTNOSTEI EKSTREMALNYKh OSADKOV, “Doklady Akademii nauk””, Doklady Akademii Nauk, 2017, no. 5, 604  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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