Log shifted gamma approximation to lognormal sum distributions

This paper proposes the log shifted gamma (LSG) approximation to model the sum of M lognormal distributed random variables. The closed-form probability density function (PDF) of the resulting LSG random variable (RV) is presented and its parameters are derived from those of the M individual lognormal RV by using an iterative moment matching technique. Simulation results on the cumulative distribution function (CDF) of sum of M lognormal random variables in different conditions are used as reference curves to compare various approximation techniques. LSG approximation is found to provide better accuracy over a wide CDF range, especially for large M and/or standard deviation.