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The joint asymptotic distribution of the k-smallest sample spacings

Published online by Cambridge University Press:  14 July 2016

Lionel Weiss
Lionel Weiss*
Affiliation:
Cornell University
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Extract

Suppose Q1⋆, … Qn⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 442 - 448
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Abramson, L. (1966) The distribution of the smallest sample spacing. (Abstract). Ann. Math. Statist. 37, 1421.Google Scholar
[2] Cramer, H. (1951) Mathematical Methods of Statistics. Princeton University Press, Princeton, New Jersey.Google Scholar
[3] Efron, B. (1964) Problems in probability of a geometrical nature. Unpublished report.Google Scholar
[4] Weiss, L. (1959) The limiting joint distribution of the largest and smallest sample spacings. Ann. Math. Statist. 30, 590–593.Google Scholar