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arXiv · 1802.10330

Extreme-value copulas associated with the expected scaled maximum of independent random variables

Jan-Frederik Mai
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Abstract

It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are independent and identically distributed, min-stable multivariate exponential random vectors with the associated survival extreme-value copulas are shown to arise as finite-dimensional margins of an infinite exchangeable sequence in the sense of De Finetti's Theorem. The associated latent factor is a stochastic process which is strongly infinitely divisible with respect to time, which induces a bijection from the set of distribution functions F of non-negative random variables with finite mean to the set of L\'evy measures on the positive half-axis. Since the Gumbel and the Galambos copula are the most popular examples of this construction, the investigation of this bijection contributes to a further understanding of their well-known analytical similarities. Furthermore, a simulation algorithm based on the latent factor representation is developed, if the support of F is bounded. Especially in large dimensions, this algorithm is efficient because it makes use of the De Finetti structure.

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Jan-Frederik Mai. 2018-02-28. Extreme-value copulas associated with the expected scaled maximum of independent random variables. https://doi.org/10.1016/j.jmva.2018.02.005

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