To assess the performance of maximum-likelihood (ML) based Nakagami m parameter estimators, current methods rely on Monte Carlo simulation. In order to enable the analytical performance evaluation of ML-based m parameter estimators, we study the statistical properties of a parameter Δ, which is defined as the log-ratio of the arithmetic mean to the geometric mean for Nakagami-m fading power. Closed-form expressions are derived for the probability density function (PDF) of Δ. It is found that for large sample size, the PDF of Δ can be well approximated by a two-parameter Gamma PDF.