On the convergence of the chi square and noncentral chi square distributions to the normal distribution

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On the convergence of the chi square and noncentral chi square distributions to the normal distribution

Horgan, Donagh; Murphy, Colin C.
Date: 2013-12
Copyright: ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Related: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6663749&isnumber=6692867
Citation: Horgan, D.; Murphy, C.C., "On the Convergence of the Chi Square and Noncentral Chi Square Distributions to the Normal Distribution," IEEE Communications Letters, vol.17, no.12, pp.2233-2236, December 2013. doi: 10.1109/LCOMM.2013.111113.131879
Published Version: 10.1109/LCOMM.2013.111113.131879

Abstract:

A simple and novel asymptotic bound for the maximum error resulting from the use of the central limit theorem to approximate the distribution of chi square and noncentral chi square random variables is derived. The bound enables the quick calculation of the number of degrees of freedom required to ensure a given approximation error, and is significantly tighter than bounds derived using the Berry-Esseen theorem. An application to widely-used approximations for the decision probabilities of energy detectors is also provided.

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