Some bivariate uniform distributions

Abstract

Bivariate uniform distributions with dependent components are readily derived by distribution function transformations of the components of non-uniform dependent continuous bivariate random variables (X,Y). Contour plots of joint density functions show the various, and varying, forms of dependence which can arise from different distributional forms for (X,Y) and aids the choice of bivariate uniform distributions as empirical models.

Keywords:

• bivariate uniform distributions
• Distribution function transformations
• density function plots
• Morgenstern
• Plackett
• Gumbel-exponenciai
• normal and Cauchy bivariate distributions