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Inform. Primen., 2013, Volume 7, Issue 1, Pages 105–115 (Mi ia250)  

This article is cited in 17 scientific papers (total in 17 papers)

Variance-generalized-gamma-distributions as limit laws for random sums

L. M. Zaksa, V. Yu. Korolevbc

a Department of Modeling and Mathematical Statistics, Alpha-Bank
b Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
c IPI RAN

Abstract: A general theorem is proved establishing necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to variance-mean mixtures of normal laws. As a corollary, necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to variance-generalized-gamma-distributions are obtained. For a special case of continuous-time random walks generated by compound doubly stochastic Poisson processes, convergence rate estimates are presented.

Keywords: random sum; generalized hyperbolic distribution; generalized inverse Gaussian distribution; generalized gamma-distribution; variance-generalized-gamma-distribution; mixture of probability distributions; identifiable mixtures; additively closed family; convergence rate estimate.

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Citation: L. M. Zaks, V. Yu. Korolev, “Variance-generalized-gamma-distributions as limit laws for random sums”, Inform. Primen., 7:1 (2013), 105–115

Citation in format AMSBIB
\Bibitem{ZakKor13}
\by L.~M.~Zaks, V.~Yu.~Korolev
\paper Variance-generalized-gamma-distributions as~limit laws for~random sums
\jour Inform. Primen.
\yr 2013
\vol 7
\issue 1
\pages 105--115
\mathnet{http://mi.mathnet.ru/ia250}


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    This publication is cited in the following articles:
    1. S. V. Bogomolov, I. G. Gudich, “Towards a stochastic diffusion gas model verification”, Math. Models Comput. Simul., 6:3 (2014), 305–316  mathnet  crossref  mathscinet
    2. M. E. Grigoreva, V. Yu. Korolev, “O skhodimosti raspredelenii sluchainykh summ k skoshennym eksponentsialno-stepennym zakonam”, Inform. i ee primen., 7:4 (2013), 66–74  mathnet  crossref  elib
    3. Gorshenin A.K. Korolev V.Yu. Zeifman A.I. Shorgin S.Ya. Chertok A.V. Evstafyev A.I. Korchagin A.Yu., “Modelling Stock Order Flows with Non-Homogeneous Intensities From High-Frequency Data”, 11th International Conference of Numerical Analysis and Applied Mathematics 2013, Pts 1 and 2, AIP Conference Proceedings, 1558, ed. Simos T. Psihoyios G. Tsitouras C., Amer Inst Physics, 2013, 2394–2397  crossref  isi  scopus
    4. V. Yu. Korolev, A. Yu. Korchagin, I. A. Sokolov, A. V. Chertok, “O rabotakh v oblasti modelirovaniya informatsionnykh potokov v sovremennykh vysokochastotnykh finansovykh prilozheniyakh”, Sistemy i sredstva inform., 24:4 (2014), 63–85  mathnet  crossref  elib
    5. V. Yu. Korolev, A. Yu. Korchagin, “Modifitsirovannyi setochnyi metod razdeleniya dispersionno-sdvigovykh smesei normalnykh zakonov”, Inform. i ee primen., 8:4 (2014), 11–19  mathnet  crossref  elib
    6. A. Yu. Korchagin, “O skhodimosti sluchainykh summ nezavisimykh sluchainykh vektorov k mnogomernym obobschennym dispersionnym gamma-raspredeleniyam”, Sistemy i sredstva inform., 25:1 (2015), 127–141  mathnet  crossref  elib
    7. V. Yu. Korolev, A. K. Gorshenin, S. K. Gulev, K. P. Belyaev, “Statisticheskoe modelirovanie turbulentnykh potokov tepla mezhdu okeanom i atmosferoi s pomoschyu metoda skolzyaschego razdeleniya konechnykh normalnykh smesei”, Inform. i ee primen., 9:4 (2015), 3–13  mathnet  crossref  elib
    8. V. Yu. Korolev, A. Yu. Korchagin, I. A. Sokolov, “Obobschennye dispersionnye gamma-raspredeleniya kak modeli statisticheskikh zakonomernostei na finansovykh rynkakh”, Inform. i ee primen., 9:4 (2015), 14–28  mathnet  crossref  elib
    9. Korolev V., Gorshenin A., Gulev S., Belyaev K., “Statistical Modeling of Air-Sea Turbulent Heat Fluxes By Finite Mixtures of Gaussian Distributions”, Information Technologies and Mathematical Modelling: Queueing Theory and Applications, Itmm 2015, Communications in Computer and Information Science, 564, eds. Dudin A., Nazarov A., Yakupov R., Springer-Verlag Berlin, 2015, 152–162  crossref  isi  scopus
    10. V. Yu. Korolev, A. I. Zeifman, A. Yu. Korchagin, “Nesimmetrichnye raspredeleniya Linnika kak predelnye zakony dlya sluchainykh summ nezavisimykh sluchainykh velichin s konechnymi dispersiyami”, Inform. i ee primen., 10:4 (2016), 21–33  mathnet  crossref  elib
    11. 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
    12. 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  isi
    13. A. A. Kudryavtsev, “Baiesovskie modeli balansa”, Inform. i ee primen., 12:3 (2018), 18–27  mathnet  crossref  elib
    14. A. Gorshenin, V. Korolev, “A functional approach to estimation of the parameters of generalized negative binomial and gamma distributions”, DCCN 2018: Distributed Computer and Communication Networks, Communications in Computer and Information Science, 919, eds. V. Vishnevskiy, D. Kozyrev, Springer-Verlag, Berlin, 2018, 353–364  crossref  isi  scopus
    15. N. Feroze, M. Aslam, “A family of Bayes estimators for the parameters of the generalized gamma distribution”, Pak. J. Stat. Oper. Res., 14:4 (2018), 975+  crossref  mathscinet  isi  scopus
    16. A. A. Kudryavtsev, “O predstavlenii gamma-eksponentsialnogo i obobschennogo otritsatelnogo binomialnogo raspredelenii”, Inform. i ee primen., 13:4 (2019), 76–80  mathnet  crossref
    17. Korolev V.Yu. Zeifman A.I., “Generalized Negative Binomial Distributions as Mixed Geometric Laws and Related Limit Theorems”, Lith. Math. J., 59:3 (2019), 366–388  crossref  mathscinet  zmath  isi  scopus
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