On the Approximation of the Sum of Lognormals by a Log Skew Normal Distribution

TL;DR

This paper introduces a universal, simple analytical method to accurately approximate the sum of lognormal random variables using a log skew normal distribution, outperforming previous methods across all parameter ranges.

Contribution

The main contribution is an analytical approach for estimating log skew normal parameters, enabling highly accurate approximation of lognormal sums for all conditions.

Findings

Outperforms existing methods in accuracy

Achieves within 0.01 dB error across all cases

Works for any correlation coefficient and dB spread

Abstract

Several methods have been proposed to approximate the sum of lognormal RVs. However the accuracy of each method relies highly on the region of the resulting distribution being examined, and the individual lognormal parameters, i.e., mean and variance. There is no such method which can provide the needed accuracy for all cases. This paper propose a universal yet very simple approximation method for the sum of Lognormals based on log skew normal approximation. The main contribution on this work is to propose an analytical method for log skew normal parameters estimation. The proposed method provides highly accurate approximation to the sum of lognormal distributions over the whole range of dB spreads for any correlation coefficient. Simulation results show that our method outperforms all previously proposed methods and provides an accuracy within 0.01 dB for all cases.