Approximating a sum of random variables with a lognormal
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/645754
- author
- Mehta, Neelesh B. ; Wu, Jingxian ; Molisch, Andreas LU and Zhang, Jin
- organization
- publishing date
- 2007
- 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
- 2016-04-01 16:21:46
- date last changed
- 2022-03-30 07:20:32
@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}},
keywords = {{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}},
doi = {{10.1109/TWC.2007.051000}},
volume = {{6}},
year = {{2007}},
}