BIVARIATE DISTRIBUTIONS WITH PEARSON TYPE VII CONDITIONALS

ATHANASIOS KOTTAS, KONSTANTINOS ADAMIDIS AND SOTIRIOS LOUKAS

Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

(Received July 8, 1997; revised November 26, 1997)

Abstract. In this article the most general class of bivariate distributions such that both conditional densities are Pearson Type VII, with fixed shape parameter, is fully characterized. Some of its properties and relations with other distributions are explored. The estimation of parameters is considered by the methods of maximum likelihood and pseudolikelihood and a method for random variate generation is presented along with a simulation experiment. Bivariate and multivariate extensions of the Pearson Type VII conditionals distribution are also discussed.

Key words and phrases: Characterizations, conditional distributions, functional equations, maximum likelihood estimation, maximum pseudolikelihood estimation, Pearson Type VII distribution.