Max-Compound Cox Processes. I
- Autores: Korolev V.1,2,3, Sokolov I.2,1, Gorshenin A.2,1
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Afiliações:
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
- Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
- Hangzhou Dianzi University
- Edição: Volume 237, Nº 6 (2019)
- Páginas: 789-803
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242454
- DOI: https://doi.org/10.1007/s10958-019-04205-0
- ID: 242454
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Resumo
Extreme values are considered in samples with random size that have a mixed Poisson distribution that is generated by a doubly stochastic Poisson process. Some inequalities are proved relating the distributions and moments of extrema with those of the leading process (the mixing distribution). Limit theorems are proved for the distributions of max-compound Cox processes, and limit distributions are described. An important particular case of the negative binomial distribution of a sample size corresponding to the case where the Cox process is led by a gamma Lévy process is considered, explaining a possible genesis of tempered asymptotic models.
Sobre autores
V. Korolev
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University; Federal Research Center “Computer Science and Control”, Russian Academy of Sciences; Hangzhou Dianzi University
Autor responsável pela correspondência
Email: vkorolev@cs.msu.ru
Rússia, Moscow; Moscow; Hangzhou
I. Sokolov
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences; Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Email: vkorolev@cs.msu.ru
Rússia, Moscow; Moscow
A. Gorshenin
Federal Research Center “Computer Science and Control”, Russian Academy of Sciences; Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Email: vkorolev@cs.msu.ru
Rússia, Moscow; Moscow