On the asymptotics of discrete order statistics

J. S. Athreya, S. Sethuraman

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Let X1, X2,…, Xn be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved k times and in its spacing relative to the second highest value. Earlier and other results are discussed in context. Also, some investigation is made when the sample is Markovian. Different results emerge in this case.

Original languageEnglish (US)
Pages (from-to)243-249
Number of pages7
JournalStatistics and Probability Letters
Issue number3
StatePublished - Oct 1 2001


  • Asymptotics
  • Extreme
  • Order statistics
  • Primary 62G32
  • Secondary 47F30
  • Uniqueness

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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