The Distribution of the Size of the Maximum Cluster of Points on a Line

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Abstract

N points are independently drawn from the uniform distribution on (0, 1). Denote by E(n|N; p), the event: There exists a subinterval of (0, 1) of length p that contains at least n out of the N points. We find the probability, P(n|N; p), of E(n|N; p) for n>N/2 in terms of simple tabulated quantities.

Original languageEnglish (US)
Pages (from-to)532-538
Number of pages7
JournalJournal of the American Statistical Association
Volume60
Issue number310
DOIs
StatePublished - Jun 1965

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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