Flexible lognormal sum approximation method

Abstract

A simple and novel method is presented to approximate the distribution of the sum of independent, but not necessarily identical, lognormal random variables, by the lognormal distribution. It is shown that matching a short Gauss-Hermite approximation of the moment generating function of the lognormal sum with that of the lognormal distribution leads to an accurate lognormal sum approximation. The advantage of the proposed method over the ones in the literature, such as the Fenton-Wilkinson method, Schwartz-Yeh method, and the recently proposed Beaulieu-Xie method, is that it provides the parametric flexibility to handle the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function. The accuracy is verified using extensive simulations based on a cellular layout