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

Joseph I. Naus

doi:10.1080/01621459.1965.10480810

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

Joseph I. Naus

Research output: Contribution to journal › Article › peer-review

192 Scopus citations

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 language	English (US)
Pages (from-to)	532-538
Number of pages	7
Journal	Journal of the American Statistical Association
Volume	60
Issue number	310
DOIs	https://doi.org/10.1080/01621459.1965.10480810
State	Published - Jun 1965

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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title = "The Distribution of the Size of the Maximum Cluster of Points on a Line",

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.",

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AB - 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.

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