We consider the problem of determining the distribution of means of random probability measures which are obtained by normalizing increasing additive processes. A solution is found by resorting to a well-known inversion formula for characteristic functions due to Gurland. Moreover, expressions of the posterior distributions of those means, in the presence of exchangeable observations, are given. Finally, a section is devoted to the illustration of two examples of statistical relevance.
"Distributional results for means of normalized random measures with independent increments." Ann. Statist. 31 (2) 560 - 585, April 2003. https://doi.org/10.1214/aos/1051027881