A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function.

Characterization of a Marshall-Olkin type class of distributions

Copulas are used to specify dependence between two or more random variables. The last few years have seen a surge of developments of parametric models for copulas. Here, we provide an up-to-date and a comprehensive review of known parametric copulas as well as applications and open problems. This review is believed to be the first of its kind.

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A Compendium of Copulas

https://hal.archives-ouvertes.fr/hal-01138228/document

Marshall-Olkin type copulas generated by a global shock

A new family of Marshall-Olkin extended generalized linear exponential distribution

Shock models with recovery option via the maxmin copulas

National Natural Science Foundation of China [11171278]; Fundamental Research Funds for the Central Universities of China [2010121005]

Multivariate Generalized Marshall-Olkin Distributions and Copulas

This paper studies expectations of a supermodular function of bivariate random risks following TTE models. Comparison of such expectations are conducted based on some stochastic orders of the involved univariate survival functions in the models, and also the upper orthant-convex order between two bivariate random risks in TTE models is built. This corrects Theorem 2.3 of Mulero et al. (2010) and invalidates some results there. Some applications in actuarial science are presented as well.

Stochastic orders in time transformed exponential models with applications

This article finds that multivariate generalized Marshall-Olkin distributions are of the lack-of-partial-memory property in the sense of residual lifetimes of elder components being independent of ...

Jianhua Lin

Papers

Multivariate Generalized Marshall-Olkin Distributions and Copulas

Stochastic orders in time transformed exponential models with applications

Lack-of-partial-memory and aging properties of multivariate generalized Marshall-Olkin distributions