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

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  • Mai, Jan-Frederik

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 Lévy measures ν on (0,∞]. 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.

Suggested Citation

  • Mai, Jan-Frederik, 2018. "Extreme-value copulas associated with the expected scaled maximum of independent random variables," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 50-61.
    • Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:50-61
    DOI: 10.1016/j.jmva.2018.02.005
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    Cited by:

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    2. Mai Jan-Frederik, 2022. "About the exact simulation of bivariate (reciprocal) Archimax copulas," Dependence Modeling, De Gruyter, vol. 10(1), pages 29-47, January.

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