An absolutely continuous bivariate Topp–Leone distribution: A useful model on a bounded domain

ABSTRACT

We introduce an absolutely continuous bivariate generalization of the Topp–Leone distribution, which is a special member of the proportional reversed hazard family using a one-parameter bivariate exchangeable distribution. We show that a copula approach could also be used in defining the bivariate Topp–Leone distribution. The marginal distributions of the new bivariate distribution have also Topp–Leone distributions. We study its distributional and dependence properties. We estimate the parameters by maximum-likelihood procedure, perform a simulation study on the estimators, and apply them to a real data set. Furthermore, we give a way of generating bivariate distributions using the proposed distribution.

KEYWORDS:

• Bivariate exchangeable distribution
• Clayton copula
• distribution with bounded support
• maximum-likelihood estimation.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62E10