On the asymptotic behaviour of sample spacings
1981 ◽
Vol 90
(2)
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pp. 293-303
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SummarySuppose that we are given a random sample of size n chosen according to the uniform distribution on the unit interval. Let Zn(x) = Zn(x, ω) be the length of the unique left-closed and right-open sample spacing that contains x. The purpose of this paper is to examine the almost sure, and exceptional, growth rates of the process {Zn}. The typical maximum growth rate and the growth rate of the maximum can be of quite different orders of magnitude as is shown by the following two results.Theorem 2. With probability one we havefor almost all x.Theorem 3. With probability one we have
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1988 ◽
Vol 45
(2)
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pp. 261-270
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1994 ◽
Vol 24
(10)
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pp. 1997-2005
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2021 ◽
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2018 ◽
Vol 10
(4)
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pp. 315-325
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1993 ◽
Vol 41
(1-2)
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pp. 95-103
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