Multivariate power series distributions and Neyman's properties for multinomials

Abstract

A probelm of J. Neyman (in Classical and Contagious Discrete Distributions (G. P. Patil, Ed.), 1965, pp. 4-14) regarding a characterization of positive and negative multinomial distributions is studied in this paper. Some properties of multivariate power series distributions in general which should be of independent interest are also derived.positive multinomial distributions negative multinomial distributions power series distributions dispersion matrix linear regression