N.V.Tsilevich.
Distribution of mean values for some random measures.
Zapiski Nauchn. Semin. POMI, 240 (1997), 268-279.
English translation: J. Math. Sci. (N.Y.), 96, No. 5 (1999), 3616-3623.

Abstract. Let $\tau$ be a probability measure on $[0,1]$. We consider a generalization of the classic Dirichlet process - the random probability measure $F=\sum P_i\delta_{X_i}$, where $X=\{X_i\}$ is a sequence of independent random variables with the common distribution $\tau$ and $P=\{P_i\}$ is independent of $X$ and has the two-parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ on the unit simplex. The main result is the formula connecting the distribution $\mu$ of the random mean value $\int xdF(x)$ with the parameter measure $\tau$.

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