New continuous bivariate distributions generated from shock models

Abstract

In this paper, we develop a new class of continuous bivariate distributions based on a shock model. The proposed class is general in the sense that numerous families of distributions can be generated from it. Distributional properties of the proposed class of distributions are studied. The bivariate ageing property and the dependence structure are also analysed. It is shown that the developed bivariate distributions exhibit positive dependency and a well-defined subclass of the proposed class of bivariate distributions satisfy the bivariate lack of memory property. Specific families of distributions are derived and applied to a real data set.

KEYWORDS:

• Continuous bivariate distribution
• shock model
• dependence structure
• bivariate lack of memory property

Disclosure statement

No potential conflict of interest was reported by the author(s).

Acknowledgements

The authors thank the reviewers for their helpful comments and advice, which have improved the presentation of this paper.