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Random division of an interval

Published online by Cambridge University Press:  24 October 2008

J. G. Mauldon
J. G. Mauldon
Affiliation:
Corpus Christi CollegeOxford
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Extract

We consider n − 1 points xj (j = 1, …, n − 1) selected independently at random from the interval (0, 1), the distribution of any xj being the rectangular distribution

The points xj divide the interval (0,1) into n intervals. Let λ be the sum of the lengths of the k largest of these n intervals. It is the purpose of this paper to give the exact sampling distribution of λ for any given n and k (see equation (5)). Fisher (1) in 1929 solved the problem for k = 1. We first investigate the distribution of μ = 1 − λ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 2 , April 1951 , pp. 331 - 336
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCE

(1)Fisher, R. A.Tests of significance in harmonic analysis. Proc. Roy. Soc. A, 125 (1929), 54–9.Google Scholar