Approximating Lognormal Sum Distributions With Power Lognormal Distributions

Abstract

In wireless communications, cochannel interference is usually characterized by a sum of lognormal random variables. Since the characteristic function of a lognormal distribution lacks explicit expression, and numerical calculation of a lognormal sum distribution is very challenging, lognormal distributions are often used to approximate lognormal sum distributions. However, it has been shown that a lognormal distribution can only capture a certain part of the body of a lognormal sum distribution. To improve the accuracy of approximation of lognormal sum distributions, one must resort to non-lognormal approximations. In this paper, we propose the use of power lognormal distributions to approximate lognormal sum distributions. To illustrate the superiority of the proposed model, some numerical experimental results are provided.