Paper Info
Title
A novel highly accurate log skew normal approximation method to lognormal sum distributions
Abstract
Sums of lognormal random variables occur in many important problems in wireless communications. However, the lognormal sum distribution is known to have no close-form and is difficult to compute numerically. Several approximation methods have already been proposed to approximate the lognormal sum distribution. However, these approximation methods all have their drawbacks: some widely used approximation methods are not very accurate at the lower region, some other approximation methods require the CDF curve from Monte Carlo simulation first. In this paper, we propose a novel approximation method, namely the Log Skew Normal (LSN) approximation, to model and approximate the sum of M lognormal distributed random variables. The proposed LSN approximation method has very high accuracy in most of the region, especially in the lower region. Furthermore, this approximation method does not require the CDF curve from Monte Carlo simulation first. The closed-form probability density function (PDF) of the resulting LSN random variable is presented and its parameters are derived from those of the M individual lognormal random variables by using an moment matching technique. Simulation results on the cumulative distribution function (CDF) of sum of M lognormal random variables in different conditions are used as reference curves to compare various approximation techniques. LSN approximation is found to provide better accuracy over a wide CDF range over other approximation methods.
Year
DOI
Venue
2009
10.1109/WCNC.2009.4917525
WCNC
Keywords
Field
DocType
normal approximation method,lognormal sum distribution,m lognormal,lower region,lsn approximation,proposed lsn approximation method,cdf curve,novel approximation method,approximation method,various approximation technique,accurate log skew,monte carlo,interference,data mining,random processes,random variable,cumulative distribution function,distribution functions,monte carlo methods,lognormal distribution,probability density function,distributed computing,monte carlo simulation,wireless communication,accuracy,random variables,computational modeling,probability,approximation theory
Applied mathematics,Monte Carlo method,Random variable,Combinatorics,Approximation theory,Stochastic process,Real-time computing,Cumulative distribution function,Log-normal distribution,Probability density function,Mathematics,Approximation error
Conference
ISSN
Citations 
PageRank 
1525-3511
6
0.64
References 
Authors
7
6
Name
Order
Citations
PageRank
Zhijin Wu123530.65
Xue Li29311.57
Robert Husnay3121.22
Vasu Chakravarthy416126.35
Bin Wang51788246.68
Zhiqiang Wu6284.31