There is an infinite exchangeable sequence of random variables {Xk}k∈ℕ such that each finitedimensional distribution follows a min-stable multivariate exponential law with Galambos survival copula, named after [7]. A recent result of [15] implies the existence of a unique Bernstein function Ψ associated with {Xk}k∈ℕ via the relation Ψ(d) = exponential rate of the minimum of d members of {Xk}k∈ℕ. The present note provides the Lévy–Khinchin representation for this Bernstein function and explores some of its properties.
@article{bwmeta1.element.doi-10_2478_demo-2014-0002,
author = {Jan-Frederik Mai},
title = {A note on the Galambos copula and its associated Bernstein function},
journal = {Dependence Modeling},
volume = {2},
year = {2014},
zbl = {06313233},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_demo-2014-0002}
}
Jan-Frederik Mai. A note on the Galambos copula and its associated Bernstein function. Dependence Modeling, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_demo-2014-0002/
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