A New Approach to the Complexification of Max-Stable Distributions Using Random Angles

A. A. Goldaeva, A. V. Lebedev

Lomonosov Moscow State University

Abstract: The paper presents a new approach to the complexification of max-stable distributions. Unlike the previously known one, random angles are used. For the real and imaginary components, marginal distributions are found, and the dependence is studied using copulas and other characteristics. A limit theorem is proved.

Keywords: extreme value theory, max-stable distributions, Fréchet distribution, complex numbers, hypergeometric function, copulas.

UDC: 519.21

MSC: 60G70, 62H05

Received: 17.01.2025

DOI: 10.4213/mzm14365

 English version: Mathematical Notes, 2025, 118:3, 519–527

Bibliographic databases:

•