On bivariate pseudo-exponential distributions

A bivariate conditionally specified distribution is one in which the dependence relationship between the two random variables is accomplished by defining the distribution of one of the random variables, given the other. One such conditionally specified model is called the pseudo-exponential distribution, where both the marginal distribution of one and the conditional distribution of the other, given the first, are exponential. In this paper, a variation of this conditioning regime is introduced, and its characteristics are contrasted with the original. An example is used to demonstrate the applicability of the new model. Per-capita Gross Domestic Product (GDP) is a measure of a nation's total annual production of goods and services, divided by its population. Two variations of both the original and the new conditioning regime are applied to GDP and infant mortality data across nations and territories. Possible generalizations are considered.