Model Selection and Estimation for Lognormal Sums in Pearson´s Framework

Lognormal approximation to a sum of lognormal variables is widely addressed in wireless communications. Its discrepancy from simulation results, however, is often reported in the literature. In this correspondence, we reexamine the issue of fitting a lognormal sum in a more rigorous framework of model selection in the Pearson system. It is found that over a general parameter setting for lognormal sums, a much better approximation is the Pearson type IV distribution whose parameters can be easily determined through simple arithmetic operations. Numerical examples are presented for illustration