The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process. Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy–Stieltjes transform are achieved....

In this paper we consider the most visited site, Xt, of a Poisson process up to time t. Our point of departure from the literature on maximal spacings is our asymptotic analysis of where the maximal spacing occurs (i.e., the size of Xt) and not the size of the spacings.