On the asymptotically uniform distribution modulo 1 of extreme order statistics

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

doi:10.1111/j.1467-9574.1994.tb01431.x

On the asymptotically uniform distribution modulo 1 of extreme order statistics

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

Mathematics and Computer Science

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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 language	English
Pages (from-to)	63-70
Journal	Statistica Neerlandica
Volume	48
Issue number	1
DOIs	https://doi.org/10.1111/j.1467-9574.1994.tb01431.x
Publication status	Published - 1994

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title = "On the asymptotically uniform distribution modulo 1 of extreme order statistics",

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).",

author = "R.J.G. Wilms and J.J.A.M. Brands",

year = "1994",

doi = "10.1111/j.1467-9574.1994.tb01431.x",

language = "English",

volume = "48",

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journal = "Statistica Neerlandica",

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T1 - On the asymptotically uniform distribution modulo 1 of extreme order statistics

AU - Wilms, R.J.G.

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

PY - 1994

Y1 - 1994

N2 - 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).

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).

U2 - 10.1111/j.1467-9574.1994.tb01431.x

DO - 10.1111/j.1467-9574.1994.tb01431.x

M3 - Article

SN - 0039-0402

VL - 48

SP - 63

EP - 70

JO - Statistica Neerlandica

JF - Statistica Neerlandica

IS - 1

ER -

On the asymptotically uniform distribution modulo 1 of extreme order statistics

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