A bivariate Pareto model

Abstract

Lindley–Singpurwalla's [Multivariate distribution for the life lengths of a system sharing a common environment, J. Appl. Probab. 23 (1986), pp. 418–431] bivariate Pareto distribution is one of the most popular bivariate Pareto distributions. Sankaran and Nair [A bivariate Pareto model and its applications to reliability, Naval Res. Logist. 40 (1993), pp. 1013–1020] proposed a new bivariate Pareto distribution having Pareto marginals and containing Lindley–Singpurwalla's bivariate Pareto model as a special case. It also has several other interesting properties. In this paper, we re-visit Sankaran and Nair's bivariate Pareto model. We discuss several other new properties. The maximum-likelihood estimators and two-stage estimators are also investigated. We analyse two data sets for illustrative purposes. It is observed that this model can be used quite effectively for analysing competing risk data. Finally, we propose some generalizations.

Keywords:

• Pareto distribution
• bivariate hazard rate
• copula
• maximum-likelihood estimators
• competing risks

Acknowledgements

The authors thank the reviewers for their helpful suggestions.