Least squares approximation to lognormal sum distribution via piecewise linear functions

In this paper, the least squares approximation via a piecewise linear function approach is applied to solve the approximation problem of a sum of lognormal random variables. A number of linear basis functions are applied and the corresponding coefficients are specified to form a piecewise linear approximation to the sum lognormal cumulative distribution function. By using the proposed approach, arbitrary precision of the approximation can be achieved by increasing the number of basis functions. The computation complexity shows no significant increase with the increase of the number of basis functions. Simulation results exhibit a desirable performance by using the proposed approximation method through piecewise linear basis functions.