Moment Monotonicity of Weibull, Gamma and Log-normal Distributions
威布尔、伽马与对数正态分布的矩单调性
This paper investigates the moment monotonicity property of Weibull, Gamma, and Log-normal distributions. We provide the first complete mathematical proofs for the monotonicity of the function $E(X^n)^{\frac{1}{n}}$ specific to these distributions. Through the derivations, we identify a key property: in many cases, one of the two parameters defining each distribution can be effectively canceled out. This finding opens up opportunities for improved parameter estimation of…