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EXPANSIONS FOR SUMS OF RAYLEIGHS

Published online by Cambridge University Press:  30 April 2009

Christopher S. Withers  and
Saralees Nadarajah
Christopher S. Withers
Affiliation:
Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand E-mail: c.withers@irl.cri.nz
Saralees Nadarajah
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK, E-mail: mbbsssn2@manchester.ac.uk
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Abstract

Expressions for the distribution, density, and percentiles of weighted sums of Rayleigh random variables are given, including the tilted Edgeworth expansion.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 3 , July 2009 , pp. 481 - 487
Copyright
Copyright © Cambridge University Press 2009

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References

1.Beaulieu, N.C. (1990). An infinite series for the computation of the complementary probability distribution of a sum of independent random variables and its application to the sum of Rayleigh random variables. IEEE Transactions on Communications 38: 1463–1474.CrossRefGoogle Scholar
2.Daniels, H.E. (1954). Saddlepoint approximations in statistics. Annals of Mathematical Statistics 25: 631–650.CrossRefGoogle Scholar
3.Helstrom, C.W. (2000). Distribution of the sum of clutter and thermal noise. IEEE Transactions on Aerospace and Electronic Systems 36: 709–713.Google Scholar
4.Hu, J. & Beaulieu, N.C. (2005). Accurate simple closed-form approximations to Rayleigh sum distributions and densities. IEEE Communications Letters 9: 109–111.Google Scholar
5.Karagiannidis, G.K., Tsiftsis, T.A. & Sagias, N.C. (2005). A closed-form upper-bound for the distribution of the weighted sum of Rayleigh variates. IEEE Communications Letters 9: 589–591.CrossRefGoogle Scholar
6.Lugannani, R. & Rice, S. (1980). Saddle point approximation for the distribution of the sum of independent random variables. Advances in Applied Probability 12: 475–490.Google Scholar
7.Santos, J.C.S. & Yacoub, M.D. (2006). Simple precise approximations to Weibull sums. IEEE Communications Letters 10: 614–616.CrossRefGoogle Scholar
8.Simon, M.K. (2002). Probability distributions involving Gaussian random variables. Boston: Kluwer.Google Scholar
9.Stuart, A. & Ord, K. (1987). Kendall's advanced theory of statistics, Vol. 1, 5th ed.London: Griffin.Google Scholar
10.Withers, C.S. (1984). Asymptotic expansions for distributions and quantiles with power series cumulants. Journal of the Royal Statistical Society B 46: 389–396.Google Scholar
11.Withers, C.S. (2000). A simple expression for the multivariate Hermite polynomial. Statistics and Probability Letters 47: 165–169.CrossRefGoogle Scholar
12.Withers, C.S. & McGavin, P.N. (2006). Expressions for the normal distribution and repeated normals. Statistics and Probability Letters 76: 479–487.CrossRefGoogle Scholar
13.Withers, C.S. & Nadarajah, S. (2008a). MGFs for Rayleigh random variables. Wireless Personal Communications 46: 463–468.Google Scholar
14.Withers, C.S. & Nadarajah, S. (2008b). Tilted Edgeworth expansions for asymptotically normal vectors. Annals of the Institute of Statistical Mathematics, doi: 10.1007/s10463-008-0206-0.Google Scholar
15.Zhang, Q.T. (1999). A simple approach to probability of error for equal gain combiners over Rayleigh channels. IEEE Transactions on Vehicular Technology 48: 1151–1154.CrossRefGoogle Scholar