This article is cited in 3 scientific papers (total in 3 papers)
A limit theorem for geometric sums of independent nonidentically distributed random variables and its application to the prediction of the probabilities of catastrophes in nonhomogeneous flows of extremal events
Abstract:
The problem of prediction of the probabilities of catastrophes in nonhomogeneous flows of extremal events is considered. The paper develops and generalizes some methods proposed by the authors in their previous works. The flow of extremal events is considered as a marked point stochastic process with not necessarily identically distributed intervals between points (events). The proposed generalizations are based on limit theorems for geometric sums of independent not necessarily identically distributed random variables and the Balkema–Pickands–De Haan theory. Within the framework of the construction under consideration, the Weibull–Gnedenko distribution appears as a limit law for geometric sums of independent not necessarily identically distributed random variables. The efficiency of the proposed methods is illustrated by the example of their application to the problem of prediction the time of the impact of the Earth with a potentially dangerous asteroid based on the data of the IAU (International Astronomical Union) Minor Planet Center.
Keywords:
catastrophe; extremal event; random sum; geometric sum; law of large numbers; Weibull–Gnedenko distribution; Balkema–Pickands–De Haan theorem; generalized Pareto distribution.
Received: 20.10.2013
Bibliographic databases:
Document Type:
Article
Language: Russian
Citation:
M. E. Grigor'eva, V. Yu. Korolev, I. A. Sokolov, “A limit theorem for geometric sums of independent nonidentically distributed random variables and its application to the prediction of the probabilities of catastrophes in nonhomogeneous flows of extremal events”, Inform. Primen., 7:4 (2013), 11–19
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\paper A limit theorem for geometric sums of independent nonidentically distributed random variables and its application to the prediction of the probabilities of catastrophes in nonhomogeneous flows of extremal events
\jour Inform. Primen.
\yr 2013
\vol 7
\issue 4
\pages 11--19
\mathnet{http://mi.mathnet.ru/ia281}
\crossref{https://doi.org/10.14357/19922264130402}
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Linking options:
https://www.mathnet.ru/eng/ia281
https://www.mathnet.ru/eng/ia/v7/i4/p11
This publication is cited in the following 3 articles:
V. Yu. Korolev, A. Yu. Korchagin, A. I. Zeifman, “On doubly stochastic rarefaction of renewal processes”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016, ICNAAM-2016, AIP Conf. Proc., 1863, eds. T. Simos, C. Tsitouras, Amer. Inst. Phys., 2017, UNSP 090010-1
V. Yu. Korolev, A. Yu. Korchagin, A. I. Zeifman, “Teorema Puassona dlya skhemy ispytanii Bernulli so sluchainoi veroyatnostyu uspekha i diskretnyi analog raspredeleniya Veibulla”, Inform. i ee primen., 10:4 (2016), 11–20
V. Yu. Korolev, I. A. Sokolov, “Ob usloviyakh skhodimosti raspredelenii ekstremalnykh poryadkovykh statistik k raspredeleniyu Veibulla”, Inform. i ee primen., 8:3 (2014), 3–11