| Abstract |
For a sample of size n from a random discrete distribution P on the real line R, S_1 denotes the number of observations which occur only once, S_2 the number of observations which occur exactly twice,... ... , and so on. Let O_n(S^<(n)>) be the order of the random partition S^<(n)>=(S_1, …, S_n) of the positive integer n. In case P has the Dirichlet process, that is, S^<(n)> has the Ewens sampling formula, Aratia and Tavaré (1992) shows the asymptotic normality of logo_n(S^<(n)>), which is an extension of Erdös and Turán (1967). Barbour and Tavaré (1994) gives the rate of convergence. In case P has the mixture of Dirichlet processes, we give the asymptotic distribution of logO_n(S^<(n)>) and the rate of its convergence.show more
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