# A note on the Galambos copula and its associated Bernstein function

Dependence Modeling (2014)

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

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topJan-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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