Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2023, Number 3, Pages 3–8
DOI: https://doi.org/10.55959/MSU0579-9368-1-64-3-1 (Mi vmumm4533) 		 
Mathematics

Complexification of max-stable distributions

A. V. Lebedev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.55959/MSU0579-9368-1-64-3-1
Abstract: By analogy with the generalization of stable distributions to the domain of complex stability indices $\alpha$ and using the representation by a stochastic integral over a Poisson random measure, the complexification of the max-stable Frechet distribution is carried out. The result is a max-semistable distribution on the first quarter of the complex plane. Estimates are derived for marginal distribution functions.
Key words: max-stable distribution, max-semistable distribution, complex numbers, extreme value theory.
Received: 26.08.2022
English version:
Moscow University Mathematics Bulletin, 2023, Volume 78, Issue 3, Pages 105–111
DOI: https://doi.org/10.3103/S0027132223030051
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: A. V. Lebedev, “Complexification of max-stable distributions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 3, 3–8; Moscow University Mathematics Bulletin, 78:3 (2023), 105–111
Citation in format AMSBIB
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\by A.~V.~Lebedev
\paper Complexification of max-stable distributions
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2023
\issue 3
\pages 3--8
\mathnet{http://mi.mathnet.ru/vmumm4533}
\crossref{https://doi.org/10.55959/MSU0579-9368-1-64-3-1}
\zmath{https://zbmath.org/?q=an:7741290}
\elib{https://elibrary.ru/item.asp?id=53868399}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2023
\vol 78
\issue 3
\pages 105--111
\crossref{https://doi.org/10.3103/S0027132223030051}
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