On the asymptotically uniform distribution modulo 1 of extreme order statistics

R.J.G. Wilms, J.J.A.M. Brands

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Abstract

Let (Xm)81 be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of rnax (X1., Xn) to converge in distribution, as n¿8 to a random variable with a uniform distribution on [0, 1).
Original languageEnglish
Pages (from-to)63-70
JournalStatistica Neerlandica
Volume48
Issue number1
DOIs
Publication statusPublished - 1994

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Distribution Modulo 1
Extreme Order Statistics
Uniform distribution
Random variable
Fractional Parts
Identically distributed
Converge
Sufficient Conditions
Order statistics
Random variables

Cite this

Wilms, R.J.G. ; Brands, J.J.A.M. / On the asymptotically uniform distribution modulo 1 of extreme order statistics. In: Statistica Neerlandica. 1994 ; Vol. 48, No. 1. pp. 63-70.
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On the asymptotically uniform distribution modulo 1 of extreme order statistics. / Wilms, R.J.G.; Brands, J.J.A.M.

In: Statistica Neerlandica, Vol. 48, No. 1, 1994, p. 63-70.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Brands, J.J.A.M.

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AB - Let (Xm)81 be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of rnax (X1., Xn) to converge in distribution, as n¿8 to a random variable with a uniform distribution on [0, 1).

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