A reversal phenomenon in estimation based on multiple samples from the Poisson--Dirichlet distribution
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Consider two forms of sampling from a population: (i) drawing s samples of n elements with replacement and (ii) drawing a single sample of ns elements. In this paper, under the setting where the descending order population frequency follows the Poisson--Dirichlet distribution with parameter θ, we report that the magnitude relation of the Fisher information, which sample partitions converted from samples (i) and (ii) possess, can change depending on the parameters, n, s, and θ. Roughly speaking, if θ is small relative to n and s, the Fisher information of (i) is larger than that of (ii); on the contrary, if θ is large relative to n and s, the Fisher information of (ii) is larger than that of (i). The result represents one aspect of random distributions.
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