https://htn20190109.hatenablog.com/entry/2026/03/12/001520

σ固定の場合

一変量正規分布の確率関数:
$\displaystyle f(x;μ) = \dfrac{1}{\sqrt{2πσ^{2}}} \exp(- \dfrac{1}{2σ^{2}} (x-μ)^{2})$

一変量正規分布の尤度関数:
$\displaystyle L_{D}(μ)=\prod_{i=1}^n \dfrac{1}{\sqrt{2πσ^{2}}} \exp(- \dfrac{1}{2σ^{2}} (x_{i}-μ)^{2})$

一変量正規分布の負の対数尤度:
$\displaystyle - \log L_{D}(μ) = - n \log(\dfrac{1}{\sqrt{2πσ^{2}}} ) + \dfrac{1}{2σ^{2}} \sum_{i=1}^n (x_{i} - μ )^{2}$

一変量正規分布の最尤推定量:
$\displaystyle \hat{μ} = \dfrac{1}{n} \sum_{i=1}^n x_{i}$