On Neyman's conjecture: A characterization of the multinomials (Q1069236)

The paper settles a conjecture by \textit{J. Neyman} [Certain chance mechanisms involving discrete distributions. in G. P. Patil (ed.): Classical and contagious discrete distributions, Proc. Int. Sympos., McGill Univ., Montreal, Que., 1963, 4-14 (1965)] concerning a characterization of positive and negative multinomial distributions by a linear regression property of power series distributions. The authors prove by means of a counter-example that the conjecture does not hold true if certain conditions are not satisfied and they state and prove a theorem that can be thought of as the corrected version of the conjecture.