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Košir, Tomaž; Omladič, Matjaž

Singular components of shock model copulas. (English) Zbl 1473.62161

J. Comput. Appl. Math. 400, Article ID 113749, 14 p. (2022).
Summary: We present a novel approach to the study of singular components for the family of shock induced copulas which is of great importance in many applications. We concentrate on three most known families of these copulas, Marshall (also called Marshall-Olkin), reflected maxmin (RMM for short), and maxmin. Although it is generally believed that “all” shock model copulas are singular, both RMM and maxmin contain nontrivial cases of members that are absolutely continuous. It seems that for the latter family this is observed for the first time.

Cited in 2 Documents

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62N05 Reliability and life testing
60E05 Probability distributions: general theory
60E15 Inequalities; stochastic orderings

Keywords:

copula; dependence concepts; max and min copulas; transformations of distribution functions; survival analysis; shock models

Software:

CopulaModel; Mathematica
PDFBibTeX XMLCite
\textit{T. Košir} and \textit{M. Omladič}, J. Comput. Appl. Math. 400, Article ID 113749, 14 p. (2022; Zbl 1473.62161)
Full Text: DOI

References:

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