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[With respect to Bayesian approach to nonparametric inference, a prior distribution is desirable whose support includes many continuous distributions. Ferguson’s Dirichlet process satisfies this property, while a distribution being the Dirichlet process is discrete almost surely. Many works have...
[The Dirichlet process is a random probability measure and its realization is discrete almost surely. Therefore, there may be duplications among a sample from a distribution having the Dirichlet process. The distribution of this duplication is well known as the Ewens sampling formula. This...
[Nonparametric Bayes estimate of estimable parameter is obtained using the Dirichlet process as a priori. By deleting the effect of the prior, we obtain a limit of Bayes estimate. As estimators of estimable parameter, U-statistics and V-statistics are well known. These three statistics are...
[For the Ewens sampling formula, the number of distinct components is written as a sum of one and independent Bernoulli random variables almost surely. Therefore, as approximation to the distribution of the number, we consider shifted Poisson and binomial distributions. We recommend the shifted...
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