The Gumbel-Marshall-Olkin distribution

Cherubini, Umberto; Mulinacci, Sabrina

doi:10.1007/978-3-319-64221-5_2

Cited by 3 publications

(2 citation statements)

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“…This case represents a particular specification of the model considered in Cherubini and Mulinacci (2017) where more than one systemic shock is allowed affecting different subsets of the components. As proved in that paper, if K(x) = x θ , this setting implies that the observed lifetimes τ k are exponentially distributed with intensities…”

Section: Let Us Definementioning

confidence: 99%

“…One question is whether the result of the original Marshall-Olkin model, that is the exponential distribution of the observed times, may be preserved in the analysis with Archimedean dependence case. Cherubini and Mulinacci (2017) prove that the answer to this question is generally negative. The only exception is the case of a specific kind of Archimedean dependence, that is the Gumbel copula.…”

Section: Introductionmentioning

confidence: 96%

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Hierarchical Archimedean Dependence in Common Shock Models

Cherubini

Mulinacci

2020

Methodol Comput Appl Probab

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In this paper we show how to extend a simple common shock model with Archimedean dependence of the hidden variables to the non-exchangeable case. The assumption is that the hidden risk factors are linked by a hierarchical Archimedean dependence structure, possibly fully nested . We give directions about how to implement the model and to address the issue that the hidden variables must be put in descending dependence order. We show how the model can be simplified in the Gumbel-Marshall-Olkin distribution in Cherubini and Mulinacci (2017), the only case in which exponential distribution of the observed variables is preserved.

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Section: Let Us Definementioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%