Given the proposed estimators of μ and σ2, the global p-value of T statistic can be computed efficiently using the gamma distribution function as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\text{the global } p\text{-value} = 1- \Gamma\left(\mu^{2}/\sigma^{2}, \sigma^{2}/\mu\right), $$ \end{document}the globalp-value=1−Γμ2/σ2,σ2/μ, where Γ(v/2,2γ) is the gamma distribution function with the shape parameter v/2 and the scale parameter 2γ.
