Probabilities for the size of largest clusters and smallest intervals

Sylvan R. Wallenstein, Joseph I. Naus

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Given N points distributed at random on [0, 1), let npbe the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (np≥ n), for n > N/2, and for n ≤ N/2, p=1/L, L an integer. The formula for the case p=1/L is in terms of the sum of L×L determinants and is not computationally feasible for large L. The present paper derives such a computational formula.

Original languageEnglish (US)
Pages (from-to)690-697
Number of pages8
JournalJournal of the American Statistical Association
Issue number347
StatePublished - Sep 1974

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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