Estimating the distribution of a sum of independent lognormal random variables

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RVs) are compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, σ, valid for practical problems in wireless transmission, where σ is between 6 dB and 12 dB. Contrary to some previous reports, our results show that the simpler Wilkinson´s approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yeh´s 1982 approach.