Scaling of the minimum of iid random variables

T. Y. Al-Naffouri

doi:10.1016/j.sigpro.2009.02.012

Scaling of the minimum of iid random variables

T. Y. Al-Naffouri^*

^*Corresponding author for this work

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4 Scopus citations

Abstract

Several areas in signal processing and communications rely on various tools in order statistics. Studying the scaling of the extreme values of iid random variables is of particular interest as it is sometimes only possible to make meaningful statements in the large number of variables case. This paper develops a new approach to finding the scaling of the minimum of iid variables by studying the behavior of the CDF and its derivatives at one point, or equivalently by studying the behavior of the characteristic function. The theory developed is used to study the scaling of several types of random variables and is confirmed by simulations.

Original language	English (US)
Pages (from-to)	1830-1834
Number of pages	5
Journal	Signal Processing
Volume	89
Issue number	9
DOIs	https://doi.org/10.1016/j.sigpro.2009.02.012
State	Published - Sep 2009

Keywords

Characteristic function
Extreme values
Initial value theorem
Order statistics
Scaling of random variables

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering
Control and Systems Engineering
Computer Vision and Pattern Recognition

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10.1016/j.sigpro.2009.02.012

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abstract = "Several areas in signal processing and communications rely on various tools in order statistics. Studying the scaling of the extreme values of iid random variables is of particular interest as it is sometimes only possible to make meaningful statements in the large number of variables case. This paper develops a new approach to finding the scaling of the minimum of iid variables by studying the behavior of the CDF and its derivatives at one point, or equivalently by studying the behavior of the characteristic function. The theory developed is used to study the scaling of several types of random variables and is confirmed by simulations.",

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AB - Several areas in signal processing and communications rely on various tools in order statistics. Studying the scaling of the extreme values of iid random variables is of particular interest as it is sometimes only possible to make meaningful statements in the large number of variables case. This paper develops a new approach to finding the scaling of the minimum of iid variables by studying the behavior of the CDF and its derivatives at one point, or equivalently by studying the behavior of the characteristic function. The theory developed is used to study the scaling of several types of random variables and is confirmed by simulations.

KW - Characteristic function

KW - Extreme values

KW - Initial value theorem

KW - Order statistics

KW - Scaling of random variables

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SP - 1830

EP - 1834

JO - Signal Processing

JF - Signal Processing

IS - 9

ER -

Scaling of the minimum of iid random variables

Abstract

Keywords

ASJC Scopus subject areas

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