Mixture Lognormal Approximations to Lognormal Sum Distributions

Abstract

In wireless communication, co-channel interference is usually characterized by a sum of lognormal random variables. Since calculating the exact distribution of a lognormal sum has a lot of challenges, lognormal distributions are often used to approximate lognormal sum distributions. However, it has been shown that lognormal approximations can only capture a certain part of the body of a lognormal sum distribution, which implies that to accurately approximate a lognormal sum distribution, one has to resort to non-lognormal approximations. In this paper we propose to use a two-component mixture lognormal model to approximate lognormal sum distributions. Numerical examples are provided to compare the proposed mixture lognormal approximation with the existing ones.