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Weak and strong law results for a function of the spacings

Published online by Cambridge University Press:  14 July 2016

William P. McCormick
William P. McCormick*
Affiliation:
University of Georgia
*
∗ Postal address: Department of Statistics and Computer Science, Graduate Studies Building, The University of Georgia, Athens, GA 30602, USA.
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Abstract

Let be i.i.d. uniform on (0,1) random variables and define Si,n = Ui ,n–1Ui– 1,n–1, i = 1, · ··, n where the Ui –n–1 are the order statistics from a sample of size n – 1 and U 0,n–1 =0 and Un,n– 1 = 1. The Si,n are called the spacings divided by U 1,· ··,Un– 1. For a fixed integer l, set . Exact and weak limit results are obtained for the Ml,n. Further we show that with probability 1 This extends results of Cheng.

Keywords

ORDER STATISTICSPACINGSLIMITING DISTRIBUTION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 543 - 555
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research supported by the National Science Foundation under Grant MCS8202259 and by AFOSR Grant No. F49620 82 C 0009.

References

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