The Ewens sampling formula is a distribution related to the random partition of a positive integer. In this study, we investigate the issue of non-existent solutions in parameter estimation under the distribution. We derive the first and second moments matching estimators to the uniformly minimum variance unbiased estimator (UMVUE) in the asymptotic sense (hereafter referred to as Asymptotic UMUVE) using the Ewens sampling formula. A Monte Carlo simulation study is performed to evaluate the efficiency of the resulting estimators.
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