THE ERDÖS-TURÁN LAW FOR MIXTURES OF DIRICHLET PROCESSES

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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.

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Details 詳細情報について

  • CRID
    1390853649779266688
  • NII Article ID
    120005703631
  • NII Book ID
    AA10634475
  • DOI
    10.5109/1563532
  • ISSN
    2435743X
    0286522X
  • HANDLE
    2324/1563532
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • JaLC
    • IRDB
    • Crossref
    • CiNii Articles
    • OpenAIRE
  • Abstract License Flag
    Allowed

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