BIVARIATE DISTRIBUTIONS VIA A PARETO CONDITIONAL DISTRIBUTION AND A REGRESSION FUNCTION

JACEK WESOLOWSKI

Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

(Received February 22, 1994; revised June 17, 1994)

Abstract. Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate Pareto conditionals distribution are obtained.

Key words and phrases: Conditional specification, conditional distribution, regression function, bivariate probability distribution, Pareto conditional distribution, Mardia bivariate Pareto distribution, bivariate Pareto conditionals distribution.