A note on the Galambos copula and its associated Bernstein function

Jan-Frederik Mai

Dependence Modeling (2014)

  • Volume: 2, Issue: 1, page 22-29, electronic only
  • ISSN: 2300-2298

Abstract

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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.

How to cite

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Jan-Frederik Mai. "A note on the Galambos copula and its associated Bernstein function." Dependence Modeling 2.1 (2014): 22-29, electronic only. <http://eudml.org/doc/266790>.

@article{Jan2014,
abstract = {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.},
author = {Jan-Frederik Mai},
journal = {Dependence Modeling},
keywords = {Galambos copula; Bernstein function; min-stable multivariate exponential distribution; strong IDT process; infinite divisibility; MIN-stable multivariate exponential distribution},
language = {eng},
number = {1},
pages = {22-29, electronic only},
title = {A note on the Galambos copula and its associated Bernstein function},
url = {http://eudml.org/doc/266790},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Jan-Frederik Mai
TI - A note on the Galambos copula and its associated Bernstein function
JO - Dependence Modeling
PY - 2014
VL - 2
IS - 1
SP - 22
EP - 29, electronic only
AB - 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.
LA - eng
KW - Galambos copula; Bernstein function; min-stable multivariate exponential distribution; strong IDT process; infinite divisibility; MIN-stable multivariate exponential distribution
UR - http://eudml.org/doc/266790
ER -

References

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  15. [15] J.-F. Mai, M. Scherer, Characterization of extendible distributions with exponential minima via stochastic processes that are infinitely divisible with respect to time, Extremes, in press, DOI 10.1007/s10687-013-0175-4 (2013). [Crossref] 
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