Abstract
Let Τ 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={Xi} is a sequence of independent random variables with the common distribution Τ and P={Pi} is independent of X and has the two-parameter Poisson-Dirichlet distribution PD(α, θ) on the unit simplex. The main result is the formula connecting the distribution Μ of the random mean value ∫ xdF(x) with the parameter measure Τ.
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 268–279.
Supported by the Russian Foundation for Basic Research, grant 96-01-00676.
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Tsilevich, N.V. Distribution of the mean value for certain random measures. J Math Sci 96, 3616–3623 (1999). https://doi.org/10.1007/BF02175838
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DOI: https://doi.org/10.1007/BF02175838