Fitting the Log Skew Normal to the Sum of Independent Lognormals Distribution

TL;DR

This paper introduces a simple, accurate method for fitting the log skew normal distribution to sums of lognormal variables, improving approximation accuracy while reducing computational complexity in wireless communication applications.

Contribution

It proposes a novel fitting technique using moments and tail slopes, offering a simpler yet equally accurate alternative to existing methods for approximating lognormal sums.

Findings

Method achieves comparable accuracy to existing approaches

Simplifies the fitting process with reduced computational effort

Validated through outage probability calculation example

Abstract

Sums of lognormal random variables (RVs) occur in many important problems in wireless communications especially in interferences calculation. Several methods have been proposed to approximate the lognormal sum distribution. Most of them requires lengthy Monte Carlo simulations, or advanced slowly converging numerical integrations for curve fitting and parameters estimation. Recently, it has been shown that the log skew normal distribution can offer a tight approximation to the lognormal sum distributed RVs. We propose a simple and accurate method for fitting the log skew normal distribution to lognormal sum distribution. We use moments and tails slope matching technique to find optimal log skew normal distribution parameters. We compare our method with those in literature in terms of complexity and accuracy. We conclude that our method has same accuracy than other methods but more simple. To further validate our approach, we provide an example for outage probability calculation in lognormal shadowing environment based on log skew normal approximation.