A fast method to seek the mean and variance of the summation of lognormal variables

Abstract

The sum of lognormal variables has been a topic of interest in several fields of research such as engineering, biology and finance, among others. For example, in the field of telecommunications, the aggregate interference of radio frequency signals is modeled as a sum of lognormal variables. To date, there is no closed expression for the probability distribution function (PDF) of this sum. Several authors have proposed approximations for this PDF, with which they calculate the mean and variance. However, each method has limitations in its range of parameters for mean, variance and number of random variables to be added. In other cases, long approximations as power series are used, which makes the analytical treatment impractical and reduces the computational performance of numerical operations.  This paper shows an alternative method for calculating the mean and variance of the sum of lognormal random variables from a computational performance approach. Our method has been evaluated extensively by Monte Carlo simulations. As a result, this method is computationally efficient and yields a low approximation error computation for a wide range of mean values, variances and number of random variables.