Bivariate Continuous Distributions with Specified Conditional Hazard Functions

In this article, we describe the construction of a bivariate continuous distribution based on the specification of conditional hazard functions. We present a functional equation whose solution determines the underlying bivariate distribution. Through this approach, for example, we present a characterization of the bivariate exponential distribution of Arnold and Strauss (1988) in that it is the only bivariate continuous distribution having both conditional hazard functions as constants. Some other interesting examples are presented with different choices of conditional hazard functions such as those of Rayleigh, Weibull, Pareto, and Makeham.