Least Squares Quadratic (LSQ) Approximation to Lognormal Sum Distributions

In this paper, least squares (LS) approximation approach is used to solve the approximation problem of a sum of lognormal random variables. It is shown that Least Squares Quadratic (LSQ) approximation exhibits an excellent match with the simulation results in a wide range of the distributions of the summands. Using the coefficients obtained from the LSQ method, closedform expressions for the cumulative distribution function (CDF) and the probability density function (pdf) for the sum random variable and its logarithm, are presented.