RANDOM DISCRETE-DISTRIBUTIONS INVARIANT UNDER SIZE-BIASED PERMUTATION

Invariance of a random discrete distribution under size-biased permuta tion is equivalent to a conjunction of symmetry conditions on its fini te-dimensional distributions. This is applied to characterize residual allocation models with independent factors that are invariant under s ize-biased permutation. Apart from some exceptional cases and minor mo difications, such models form a two-parameter family of generalized Di richlet distributions.