An error bound for moment matching methods of lognormal sum distributions

To evaluate the distribution function of a sum of lognormal random variables it is common to use approximation methods based on moment matching. These include the classical and simple Fenton–Wilkinson (FW) method, which approximates the sum with a single lognormal variable, having the first two moments matched. In this letter, we give a closed-form bound for the error of the distribution function, resulting from moment matching methods. Numerical evaluation for a typical CDMA case, shows that the bound becomes tight for large processing gains. The error bound can also be used to find bounds on the outage probability.