V. Yu. Korolev, “Convergence of random sequences with independent random indices. II”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 907–910; Theory Probab. Appl., 40:4 (1995), 770

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Teoriya Veroyatnostei i ee Primeneniya, 1995, Volume 40, Issue 4, Pages 907–910 (Mi tvp3685)

This article is cited in 31 scientific papers (total in 31 papers)

Short Communications

Convergence of random sequences with independent random indices. II

V. Yu. Korolev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Full-text PDF (294 kB) Citations (31)

Abstract: Necessary and sufficient conditions are obtained for the convergence of some statistics constructed from samples with random sizes.

Keywords: random sequences with random indices, weak convergence, samples with random sizes, order statistics, asymptotically normal statistics.

Received: 10.03.1994

English version:
Theory of Probability and its Applications, 1995, Volume 40, Issue 4, Pages 770–772
DOI: https://doi.org/10.1137/1140089

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. Yu. Korolev, “Convergence of random sequences with independent random indices. II”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 907–910; Theory Probab. Appl., 40:4 (1995), 770–772

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp3685

https://www.mathnet.ru/eng/tvp/v40/i4/p907

Cycle of papers

Convergence of random sequences with the independent random indices. I
V. Yu. Korolev
Teor. Veroyatnost. i Primenen., 1994, 39:2, 313–333
Convergence of random sequences with independent random indices. II
V. Yu. Korolev
Teor. Veroyatnost. i Primenen., 1995, 40:4, 907–910

This publication is cited in the following 31 articles:

Victor Yu. Korolev, “The Logistic Distribution as a Limit Law for Random Sums and Statistics Constructed from Samples with Random Sizes”, Mathematics, 12:23 (2024), 3775
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
Victor Korolev, “Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions”, Mathematics, 11:13 (2023), 2890
Gorshenin A., Kuzmin V., “Statistical Feature Construction For Forecasting Accuracy Increase and Its Applications in Neural Network Based Analysis”, Mathematics, 10:4 (2022), 589
Khokhlov Yu. Korolev V., “On a Multivariate Analog of the Zolotarev Problem”, Mathematics, 9:15 (2021), 1728
V. Yu. Korolev, “O raspredelenii otnosheniya summy elementov vyborki, prevoskhodyaschikh nekotoryi porog, k summe vsekh elementov vyborki. I”, Inform. i ee primen., 14:3 (2020), 35–43
Gorshenin A., Korolev V., Zeifman A., “Modeling Particle Size Distribution in Lunar Regolith Via a Central Limit Theorem For Random Sums”, Mathematics, 8:9 (2020), 1409
Korolev V., Gorshenin A., “Probability Models and Statistical Tests For Extreme Precipitation Based on Generalized Negative Binomial Distributions”, Mathematics, 8:4 (2020), 604
V. Korolev, A. Gorshenin, A. Zeifman, “On Mixture Representations for the Generalized Linnik Distribution and Their Applications in Limit Theorems”, J Math Sci, 246:4 (2020), 503
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
Korolev V., Gorshenin A., Belyaev K., “Statistical Tests For Extreme Precipitation Volumes”, Mathematics, 7:7 (2019), 648
Bening V.E. Korolev V.Yu. Zeifman A.I., “Calculation of the Deficiency of Some Statistical Estimators Constructed From Samples With Random Sizes”, Colloq. Math., 157:2 (2019), 157–171
V. Yu. Korolev, “Nekotorye svoistva raspredeleniya Mittag-Lefflera i svyazannykh s nim protsessov”, Inform. i ee primen., 11:4 (2017), 26–37
Korolev V.Yu. Zeifman A.I., “Convergence of Statistics Constructed From Samples With Random Sizes to the Linnik and Mittag-Leffler Distributions and Their Generalizations”, J. Korean Stat. Soc., 46:2 (2017), 161–181
Korolev V. Gorshenin A. Korchagin A. Zeifman A., “Generalized Gamma Distributions as Mixed Exponential Laws and Related Limit Theorems”, Proceedings of the 31st European Conference on Modelling and Simulation (ECMS 2017), ed. Paprika Z. Horak P. Varadi K. Zwierczyk P. VidovicsDancs A. Radics J., European Council Modelling & Simulation, 2017, 642–648
H. Bevrani, V. Yu. Korolev, “Estimation of availability function using Student distribution”, Theory Probab. Appl., 61:2 (2017), 327–335
V. Yu. Korolev, “Limit distributions for doubly stochastically rarefied renewal processes and their properties”, Theory Probab. Appl., 61:4 (2017), 649–664
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
Korolev V.Yu. Zeifman A.I., “On convergence of the distributions of random sequences with independent random indexes to variance–mean mixtures”, Stoch. Models, 32:3 (2016), 414–432
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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