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Approximating a sum of random variables with a lognormal

Mehta, Neelesh B.; Wu, Jingxian; Molisch, Andreas LU and Zhang, Jin (2007) In IEEE Transactions on Wireless Communications 6(7). p.2690-2699
Abstract
A simple, novel, and general method is presented in this paper for approximating the sum of independent or arbitrarily correlated lognormal random variables (RV) by a single lognormal RV. The method is also shown to be applicable for approximating the sum of lognormal-Rice and Suzuki RVs by a single lognormal RV. A sum consisting of a mixture of the above distributions can also be easily handled. The method uses the moment generating function (MGF) as a tool in the approximation and does so without the extremely precise numerical computations at a large number of points that were required by the previously proposed methods in the literature. Unlike popular approximation methods such as the Fenton-Wilkinson method and the Schwartz-Yeh... (More)
A simple, novel, and general method is presented in this paper for approximating the sum of independent or arbitrarily correlated lognormal random variables (RV) by a single lognormal RV. The method is also shown to be applicable for approximating the sum of lognormal-Rice and Suzuki RVs by a single lognormal RV. A sum consisting of a mixture of the above distributions can also be easily handled. The method uses the moment generating function (MGF) as a tool in the approximation and does so without the extremely precise numerical computations at a large number of points that were required by the previously proposed methods in the literature. Unlike popular approximation methods such as the Fenton-Wilkinson method and the Schwartz-Yeh method, which have their own respective short-comings, the proposed method provides the parametric flexibility to accurately approximate different portions of the lognormal sum distribution. The accuracy of the method is measured both visually, as has been done in the literature, as well as quantitatively, using curve-fitting metrics. An upper bound on the sensitivity of the method is also provided. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
moment generating function, characteristic function, moment methods, lognormal-Rice distribution, Suzuki distribution, lognormal distribution, correlation, approximation methods, co-channel, interference
in
IEEE Transactions on Wireless Communications
volume
6
issue
7
pages
2690 - 2699
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000247984000039
  • scopus:34547485292
ISSN
1536-1276
DOI
10.1109/TWC.2007.051000
language
English
LU publication?
yes
id
f90bc38c-e15d-41ca-9fde-2379e07b81cf (old id 645754)
date added to LUP
2007-12-15 14:38:43
date last changed
2017-10-01 04:44:10
@article{f90bc38c-e15d-41ca-9fde-2379e07b81cf,
  abstract     = {A simple, novel, and general method is presented in this paper for approximating the sum of independent or arbitrarily correlated lognormal random variables (RV) by a single lognormal RV. The method is also shown to be applicable for approximating the sum of lognormal-Rice and Suzuki RVs by a single lognormal RV. A sum consisting of a mixture of the above distributions can also be easily handled. The method uses the moment generating function (MGF) as a tool in the approximation and does so without the extremely precise numerical computations at a large number of points that were required by the previously proposed methods in the literature. Unlike popular approximation methods such as the Fenton-Wilkinson method and the Schwartz-Yeh method, which have their own respective short-comings, the proposed method provides the parametric flexibility to accurately approximate different portions of the lognormal sum distribution. The accuracy of the method is measured both visually, as has been done in the literature, as well as quantitatively, using curve-fitting metrics. An upper bound on the sensitivity of the method is also provided.},
  author       = {Mehta, Neelesh B. and Wu, Jingxian and Molisch, Andreas and Zhang, Jin},
  issn         = {1536-1276},
  keyword      = {moment generating function,characteristic function,moment methods,lognormal-Rice distribution,Suzuki distribution,lognormal distribution,correlation,approximation methods,co-channel,interference},
  language     = {eng},
  number       = {7},
  pages        = {2690--2699},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Wireless Communications},
  title        = {Approximating a sum of random variables with a lognormal},
  url          = {http://dx.doi.org/10.1109/TWC.2007.051000},
  volume       = {6},
  year         = {2007},
}