Log-Shifted Gamma Approximation to Lognormal Sum Distributions

This paper proposes the log-shifted gamma (LSG) approximation to model the sum of M lognormally distributed random variables (RVs). The closed-form probability density function of the resulting LSG RV is presented, and its parameters are directly derived from those of the M individual lognormal RVs by using an iterative moment-matching technique without the need for curve fitting of computer-generated distributions. Simulation and analytical results on the cumulative distribution function (cdf) of the sum of M lognormal RVs in different conditions indicate that the proposed LSG approximation can provide better accuracy than other lognormal approximations over a wide cdf range, especially for large M and/or standard deviation.