On the limiting distribution of fractional parts of extreme order statistics

R.J.G. Wilms

On the limiting distribution of fractional parts of extreme order statistics

R.J.G. Wilms

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Abstract

Let X_2, X_2, ... be a sequence of independent and identically distributed random variables with distribution function F, and suppose that F belongs to the domain of attraction of an extreme value distribution. We give (additional) sufficient conditions on F for the fractional part of max (X_1, X_2, ..., X_n) to converge in distribution to a random variable with a uniform distribution on [0,1), or to diverge in distribution as n -> infinity. Key Words & Phrases: distribution (modulo 1), extreme value theory, Fourier-Stieltjes coefficients, fractional part.

Original language	English
Place of Publication	Eindhoven
Publisher	Technische Universiteit Eindhoven
Number of pages	15
Publication status	Published - 1993

Publication series

Name	Memorandum COSOR
Volume	9313
ISSN (Print)	0926-4493

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title = "On the limiting distribution of fractional parts of extreme order statistics",

abstract = "Let X_2, X_2, ... be a sequence of independent and identically distributed random variables with distribution function F, and suppose that F belongs to the domain of attraction of an extreme value distribution. We give (additional) sufficient conditions on F for the fractional part of max (X_1, X_2, ..., X_n) to converge in distribution to a random variable with a uniform distribution on [0,1), or to diverge in distribution as n -> infinity. Key Words & Phrases: distribution (modulo 1), extreme value theory, Fourier-Stieltjes coefficients, fractional part.",

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AU - Wilms, R.J.G.

PY - 1993

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N2 - Let X_2, X_2, ... be a sequence of independent and identically distributed random variables with distribution function F, and suppose that F belongs to the domain of attraction of an extreme value distribution. We give (additional) sufficient conditions on F for the fractional part of max (X_1, X_2, ..., X_n) to converge in distribution to a random variable with a uniform distribution on [0,1), or to diverge in distribution as n -> infinity. Key Words & Phrases: distribution (modulo 1), extreme value theory, Fourier-Stieltjes coefficients, fractional part.

AB - Let X_2, X_2, ... be a sequence of independent and identically distributed random variables with distribution function F, and suppose that F belongs to the domain of attraction of an extreme value distribution. We give (additional) sufficient conditions on F for the fractional part of max (X_1, X_2, ..., X_n) to converge in distribution to a random variable with a uniform distribution on [0,1), or to diverge in distribution as n -> infinity. Key Words & Phrases: distribution (modulo 1), extreme value theory, Fourier-Stieltjes coefficients, fractional part.

M3 - Report

T3 - Memorandum COSOR

BT - On the limiting distribution of fractional parts of extreme order statistics

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -