Approximations for distributions of scan statistics

Joseph I. Naus

Research output: Contribution to journalArticlepeer-review

115 Scopus citations


Certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length. This article gives an approximation that is highly accurate for several of these distributions. Applications include the maximum cluster of points on a line or circle, multiple coverage by subintervals or subarcs of fixed size, the length of the longest success run in Bernoulli trials, and the generalized birthday problem.

Original languageEnglish (US)
Pages (from-to)177-183
Number of pages7
JournalJournal of the American Statistical Association
Issue number377
StatePublished - Mar 1982

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Generalized birthday probability
  • Longest run
  • Maximum cluster
  • Multiple coverage
  • Scan statistics
  • Window statistics


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