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The Ewens sampling formula is well-known as a distribution of a random partition of the positive integer n. For the number of distinct components of the Ewens sampling formula, we derive its Edgeworth expansion. It is different from the Edgeworth expansion for the sum of independent and identicallydistributed random variables. It contains the digamma function of the parameter of the Ewens sampling formula. Especially, for the random permutation, the Edgeworth expansion contains Euler’s constant. The Edgeworth expansion is examined numericallyusing its graph.

Edgeworth Expansions for the Number of Distinct Components Associated with the Ewens Sampling Formula