Probability density function of logarithmic ratio of arithmetic mean to geometric mean for Nakagami-m fading power

In this work, we study the statistical properties of a parameter Δ, which is defined as the logarithmic ratio of the arithmetic mean to the geometric mean for the Nakagami-m fading power. This parameter is useful in studying the maximum-likelihood (ML) based estimation of the Nakagami m fading parameter. Closed-form expressions are derived for the moment generating function and the probability density function (PDF) of the parameter Δ. For large sample size, it is found that the PDF of the parameter Δ can be well approximated by a two-parameter Gamma PDF. This approximation is validated by the Kolmogorov-Smirnov test.