Skip to main content Accessibility help
×
Home
Hostname: page-component-544b6db54f-s4m2s Total loading time: 0.219 Render date: 2021-10-18T05:37:07.688Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

EXPANSIONS FOR SUMS OF RAYLEIGHS

Published online by Cambridge University Press:  30 April 2009

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

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
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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: 14631474.CrossRefGoogle Scholar
2.Daniels, H.E. (1954). Saddlepoint approximations in statistics. Annals of Mathematical Statistics 25: 631650.CrossRefGoogle Scholar
3.Helstrom, C.W. (2000). Distribution of the sum of clutter and thermal noise. IEEE Transactions on Aerospace and Electronic Systems 36: 709713.CrossRefGoogle Scholar
4.Hu, J. & Beaulieu, N.C. (2005). Accurate simple closed-form approximations to Rayleigh sum distributions and densities. IEEE Communications Letters 9: 109111.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: 589591.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: 475490.CrossRefGoogle Scholar
7.Santos, J.C.S. & Yacoub, M.D. (2006). Simple precise approximations to Weibull sums. IEEE Communications Letters 10: 614616.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: 389396.Google Scholar
11.Withers, C.S. (2000). A simple expression for the multivariate Hermite polynomial. Statistics and Probability Letters 47: 165169.CrossRefGoogle Scholar
12.Withers, C.S. & McGavin, P.N. (2006). Expressions for the normal distribution and repeated normals. Statistics and Probability Letters 76: 479487.CrossRefGoogle Scholar
13.Withers, C.S. & Nadarajah, S. (2008a). MGFs for Rayleigh random variables. Wireless Personal Communications 46: 463468.CrossRefGoogle 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: 11511154.CrossRefGoogle Scholar
1
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

EXPANSIONS FOR SUMS OF RAYLEIGHS
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

EXPANSIONS FOR SUMS OF RAYLEIGHS
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

EXPANSIONS FOR SUMS OF RAYLEIGHS
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *