Bivariate Extension of Lomax and Finite Range Distributions through Characterization Approach

Abstract

In the univariate setup the Lomax distribution is being widely used for stochastic modelling of decreasing failure rate life components. It also serves as a useful model in the study of labour turnover, queueing theory, and biological analysis. A bivariate extension of the Lomax distribution given in Lindley and Singpurwalla (1986) fails to cover the case of independence. Our present attempt is to obtain the unique determination of a bivariate Lomax distribution through characterization results. In this process we also obtain bivariate extensions of the exponential and a finite range distributions. The bivariate Lomax distribution thus obtained is a member of the Arnold (1990) flexible family of Pareto distributions and the bivariate exponential distribution derived here is identical with that of Gumbel (1960). Various properties of the proposed extensions are presented.