TY - JOUR

T1 - Distribution of the mean value for certain random measures

AU - Tsilevich, N. V.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Let τ be a probability measure on [0,1]. We consider a generalization of the classic Dirichlet process - the random probability measure F = Σ Pi δxi, where X = {Xi} is a sequence of independent random variables with the common distribution r and P = {P i} 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 T.

AB - Let τ be a probability measure on [0,1]. We consider a generalization of the classic Dirichlet process - the random probability measure F = Σ Pi δxi, where X = {Xi} is a sequence of independent random variables with the common distribution r and P = {P i} 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 T.

UR - http://www.scopus.com/inward/record.url?scp=53149110765&partnerID=8YFLogxK

U2 - 10.1007/BF02175838

DO - 10.1007/BF02175838

M3 - Article

AN - SCOPUS:53149110765

VL - 96

SP - 3616

EP - 3623

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -