A Strict Approach to Approximating Lognormal Sum Distributions

In this paper, the least squares (LS) approximation approach is applied to solve the approximation problem of a sum of lognormal random variables (RV). The least squares curve fitting technique is first used to obtain the approximated closed-form pdf of the sum RV. The second time use of the least squares curve fitting technique brings the explicit closed-form expressions of the coefficients as a function of the number of the summands and the dB spread of the summands. Simulation results show that the proposed approximation exhibits a good match with the simulation results in the interested range of the distributions of the summands. Furthermore, errors due to a mixed use of the sum RV in the domain of the original variable and the domain of the logarithm are pointed out and the corrected results are presented