Tailfree and Neutral Random Probabilities and Their Posterior Distributions

Abstract

The random distribution function $F$ and its law is said to be neutral to the right if $F(t_1), \lbrack F(t_2) - F(t_1) \rbrack/\lbrack 1 - F(t_1)\rbrack, \cdots, \lbrack F(t_k) - F(t_{k-1}) \rbrack/\lbrack 1 - F(t_{k-1}) \rbrack$ are independent whenever $t_1 < \cdots < t_k$. The posterior distribution of a random distribution function neutral to the right is shown to be neutral to the right. Characterizations of these random distribution functions and connections between neutrality to the right and general concepts of neutrality and tailfreeness (tailfreedom) are given.