Estimation of typical sum of lognormal random variables using log shifted gamma approximation

The sum of lognormal distributions is a well-known problem that no closed-form expression exists and it is difficult to evaluate numerically. In this paper, log shifted gamma (LSG) approximation method is proposed to represent the sum of lognormal distributions and to derive a closed-form expression of the typical value of the sum. Illustrative results show that the LSG model provides much more accurate approximation than other previous methods for a wide range of lognormal variances.