Simple α-μ approximation to lognormal sums

Abstract

In this paper, we adopt the α-μ distribution to approximate the statistic distribution of the sum of independent and possibly non-identically distributed lognormal variables, and obtain the shape and scale parameters using both the moment matching method and Non-linear Least Square Method. Finally, we evaluate the performance via numerical simulations, the results illustrate that the α-μ approximation fits well the sum of the lognormal variables.