On approximating the distribution of a sum of independent lognormal random variables

The authors investigate four approaches that can be used to compute the distribution of a sum of independent lognormal random variables (RVs). Simulation results for the complementary cumulative distribution function (CDF) of sums of independent lognormal RVs are used for verification and comparison. The aim is to determine which method is best for computing the complementary cumulative distribution function. The problem is formally stated and some observations regarding different approaches to the problem are given. Three related methods based on lognormal approximation of the sum CDF are described and assessed. An assessment of a different approach. Farley´s method, that has been reported in the literature is described. An intuitive basis for the method is also given. A comparative examination of the different methods is presented. This leads to an explanation of the differences of the approximations.