Accurate simple closed-form approximations to distributions and densities of lognormal sum random variables

Abstract

Sums of lognormal random variables occur in many wireless communications problems, in part, because a shadowing environment is well modeled by a lognormal distribution. A closed-form expression does not exist for the lognormal characteristic function; as a result no closed-form expression can be derived for the sum distribution. Many approximations exist that are based on approximating a sum of lognormal random variables as another lognormal random variable. A new method for calculating an approximation to a lognormal sum distribution, based on curve fitting on lognormal probability paper is introduced in this paper. Accurate, simple closed-form approximations to distributions and densities of lognormal sum random variables are presented.