On the Variability Estimation of Lognormal Distribution Based on Sample Harmonic and Arithmetic Means

TL;DR

This paper introduces an unbiased estimator for the squared coefficient of variation of a lognormal distribution, derived from the ratio of sample means, supported by analytical proofs and simulations.

Contribution

It provides a novel unbiased estimator for the lognormal distribution's variability based on harmonic and arithmetic means, with validation through analysis and simulations.

Findings

Estimator is unbiased for the squared coefficient of variation.

Analytical proofs confirm the estimator's properties.

Simulation results demonstrate estimator accuracy.

Abstract

For the lognormal distribution, an unbiased estimator of the squared coefficient of variation is derived from the relative ratio of sample arithmetic to harmonic means. Analytical proofs and simulation results are presented.