Probabilities for the Size of Largest Clusters and Smallest Intervals

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 an...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1974-09, Vol.69 (347), p.690-697
Main Authors: Wallenstein, Sylvan R., Naus, Joseph I.
Format: Article
Language:English
Subjects:
Coincidence
Determinants
Integers
L cells
Photons
Power lines
Probabilities
Theory and Methods
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Summary: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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1974.10480190