The two-parameter generalization of Ewens’ random partition structure

where k = m1 + . . . + mn is the total number of parts, θ > 0 is a parameter of the distribution, and θ = θ(θ + 1) . . . (θ + n − 1). For background and applications to genetics see [11, 12, 13, 6, 5, 19]. This note presents a family of distributions Pn,θ,α for random partitions of n, with two parameters θ ≥ 0 and 0 ≤ α ≤ 1. For α = 0, θ > 0, Pn,θ,0 = Pn,θ as in (1). As indicated at the end of this introduction, the case 0 < α < 1 arises naturally in the study of certain random partitions associated with stable processes with index α. In particular the case α = 1/2 is related to random partitions induced by the zeros of Brownian motion. ∗Research supported by N.S.F. Grant MCS91-07531