### Abstract

Given N points distributed at random on [0, 1), let n_{p}be the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (n_{p}≥ 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 language | English (US) |
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Pages (from-to) | 690-697 |

Number of pages | 8 |

Journal | Journal of the American Statistical Association |

Volume | 69 |

Issue number | 347 |

DOIs | |

State | Published - Jan 1 1974 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Probabilities for the size of largest clusters and smallest intervals'. Together they form a unique fingerprint.

## Cite this

Wallenstein, S. R., & Naus, J. (1974). Probabilities for the size of largest clusters and smallest intervals.

*Journal of the American Statistical Association*,*69*(347), 690-697. https://doi.org/10.1080/01621459.1974.10480190