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A characterization of the Dirichlet process. (English) Zbl 0736.62007
The purpose of this note is to point out that if the posterior mean of a random probability \(P\) given a sample \(X_ 1,\ldots,X_ n\) from \(P\) is linear in the sample empirical distribution function, then \(P\) is a Dirichlet random probability.

62E10 Characterization and structure theory of statistical distributions
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