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It is well-known that the expected scaled maximum of non-negative randomvariables with unit mean defines a stable tail dependence function associatedwith some extreme-value copula. In the special case when these random variablesare independent and identically distributed, min-stable multivariateexponential random vectors with the associated survival extreme-value copulasare shown to arise as finite-dimensional margins of an infinite exchangeablesequence in the sense of De Finetti's Theorem. The associated latent factor isa stochastic process which is strongly infinitely divisible with respect totime, which induces a bijection from the set of distribution functions F ofnon-negative random variables with finite mean to the set of L\'evy measures onthe positive half-axis. Since the Gumbel and the Galambos copula are the mostpopular examples of this construction, the investigation of this bijectioncontributes to a further understanding of their well-known analyticalsimilarities. Furthermore, a simulation algorithm based on the latent factorrepresentation is developed, if the support of F is bounded. Especially inlarge dimensions, this algorithm is efficient because it makes use of the DeFinetti structure.

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