Approximating the Distribution of a Sum of Log-normal Random Variables

Abstract

This paper introduces a process for estimating the distribution of a sum of independent and identically distributed log-normal random variables (RVs). The procedure involves using the Fenton-Wilkinson method to estimate the parameters for a single log-normal distribution that approximates the sum of log-normal RVs. Once these parameters are determined, a mixture of truncated exponentials (MTE) function is determined to approximate this distribution. The MTE parameters are stated as polynomial functions of the log-normal scale parameter. Applications to inventory management are presented that demonstrate the usefulness of the MTE approximation.