A Systematic Procedure for Accurately Approximating Lognormal-Sum Distributions

Lognormal approximation to a sum of lognormal variables has been widely adopted in wireless communications, and its justification is based on the intuition that after taking a logarithm, a lognormal sum can converge to a Gaussian variable. In this paper, we show how to fit a lognormal sum with the best candidate from a large family of distributions, including the lognormal, by resorting to a systematic procedure of model selection and parameter estimation. It is found that, over a general parameter setting, a much better approximation for the lognormal sums in the log scale is given by the Pearson type-IV distribution whose parameters can easily be determined through simple arithmetic operations. Numerical examples are presented for illustration.