Article contents
EXPANSIONS FOR SUMS OF RAYLEIGHS
Published online by Cambridge University Press: 30 April 2009
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
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
- 2
- Cited by