Simple dependent pairs of exponential and uniform random variables

Abstract

A random-coefficient linear function of two independent exponential variables yielding a third exponential variable is used in the construction of simple, dependent pairs of exponential variables. By employing antithetic exponential variables, the constructions are developed to encompass negative dependency. By employing negative exponentiation, the constructions yield simple multiplicative-based models for dependent uniform pairs. The ranges of dependency allowable in the models are assessed by correlation calculations, both of the product moment and Spearman types; broad ranges within the theoretically allowable ranges are found. Because of their simplicity, all models are particularly suitable for simulation and are free of point and line concentrations of values