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. Cl...

* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China Full list of author information is available at the end of the article Abstract In this article, we answer the question: For p, ω Î R with ω >0 and p(ω 2) ≠ 0, what are the greatest value r1 = r1(p, ω) and the least value r2 = r2(p, ω) such that the double inequality Mr1 (a, b) ...

For p ∈ R, the power mean of order p of two positive numbers a and b is defined by Mp a, b a b /2 , for p / 0, and Mp a, b √ ab, for p 0. In this paper, we answer the question: what are the greatest value p and the least value q such that the double inequality Mp a, b ≤ A a, b G a, b H1−α−β a, b ≤ Mq a, b holds for all a, b > 0 and α, β > 0 with α β < 1? Here A a, b a b /2, G a, b √ ab, and H a...