Highly Accurate Log Skew Normal Approximation to the Sum of Correlated Lognormals

TL;DR

This paper introduces a universal, simple, and highly accurate analytical approximation method for the sum of correlated lognormal random variables using log skew normal distribution, outperforming previous methods across all scenarios.

Contribution

It proposes a novel analytical approach to estimate log skew normal parameters, enabling precise approximation of correlated lognormal sums in all cases.

Findings

Achieves within 0.01 dB accuracy for all tested cases.

Outperforms existing approximation methods.

Effective across the entire range of dB spreads and correlation coefficients.

Abstract

Several methods have been proposed to approximate the sum of correlated 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 correlated 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 correlated 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.