Properties of a one-parameter family of bivariate distributions with specified marginals

Abstract

Using a family of functions first described by Frank (1979), a one-parameter family of bivariate distributions is constructed. This family has arbitrary marginals and contains the Fréchet bounds as well as the member corresponding to independent random variables, Three nonparametric measures of correlation (Spearman's rho, Ken-dall's tau, and the medial correlation coefficient) are evaluated, and a simple transformation to generate random samples from an ar-bitrary member of the family is presented.