Distribution Functions of Means of a Dirichlet Process

Let χ be a random probability measure chosen by a Dirichlet process on (R, B) with parameter α and such that ∫ xχ(dx) turns out to be a (finite) random variable. The main concern of this paper is the statement of a suitable expression for the distribution function of that random variable. Such an expression is deduced through an extension of a procedure based on the use of generalized Stieltjes transforms, originally proposed by the present authors in 1978.