On the convergence of the chi square and noncentral chi square distributions to the normal distribution
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Accepted Version
Date
2013-12
Authors
Horgan, Donagh
Murphy, Colin C.
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
Published Version
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.
Description
Keywords
Probability , Energy detection , Statistics , Random variables , Closed-form solutions , Upper bound , Cognitive radio , Spectrum sensing
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
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