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The Ewens sampling formula is well-known as a distribution of a random partition of a positive integer n or a set of integers {1, 2, ･･･ , n}. The number K_n of distinct components of the formula has ...the asymptotic normality. For its well-known form and the related form, Yamato(2013) gives their Edgeworth expansions. But, their appropriateness depend on the parameter. Using the functions of R, we consider its normal approximation suitable for any value of the parameter. As the application, we show the method to search the the maximum likelihood estimator of the parameter graphically, and gives its approximate distribution. We also consider the approximate distribution of K_n in case where the parameter of the formula is the random variable. These results are shown with the graphs.続きを見る
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