Approximating a sum of random variables with a lognormal

Summary, in English

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: Neelesh B. Mehta; Jingxian Wu; Andreas Molisch; Jin Zhang
• Department/s: Department of Electrical and Information Technology
• Publishing year: 2007
• Language: English
• Pages: 2690-2699
• Publication/Series: IEEE Transactions on Wireless Communications
• Volume: 6
• Issue: 7
• Links: http://dx.doi.org/10.1109/TWC.2007.051000
• Document type: Journal article
• Publisher: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Topic: Electrical Engineering, Electronic Engineering, Information Engineering
• Keywords: moment generating function; characteristic function; moment methods; lognormal-Rice distribution; Suzuki distribution; lognormal distribution; correlation; approximation methods; co-channel; interference
• Status: Published
• ISBN/ISSN/Other: ISSN: 1536-1276