diff --git a/docs/theory.md b/docs/theory.md new file mode 100644 index 00000000..9c9b6683 --- /dev/null +++ b/docs/theory.md @@ -0,0 +1,25 @@ +## 大数定律 + +当样本量 $n \Rightarrow \infty$ 时,样本比例 $\hat{p}$ 依概率收敛于总体比例 $p$,即 + +$$ +\hat{p} \xrightarrow{P} p +$$ + +## 连续映射定理 + +若 $g$ 是连续函数,且 $X_n \xrightarrow{P} X$,则 $g(X_n) \xrightarrow{P} g(X)$ + +## 正态分布的性质 + +1. 若 $X \sim N(\mu, \sigma^2)$,则 $P(X \le x) = \Phi(\frac{x-\mu}{\sigma})$ +2. 若 $X \sim N(\mu, \sigma^2)$,则 $P(X \ge x) = 1 - \Phi(\frac{x-\mu}{\sigma})$ +3. $\Phi(x) = 1 - \Phi(-x)$ + +## Slutsky 定理 + +令 $X_n \xrightarrow{d} X$ 且 $Y_n \xrightarrow{P} c$,其中 $c$ 为常数,则: + +1. $X_n + Y_n \xrightarrow{d} X + c$ +2. $X_nY_n \xrightarrow{d} cX$ +3. $Y_n^{-1}X_n \xrightarrow{d} c^{-1}X$,其中 $c \neq 0$ diff --git a/zensical.toml b/zensical.toml index 8bb3d6a9..020e5b5f 100644 --- a/zensical.toml +++ b/zensical.toml @@ -8,7 +8,8 @@ nav = [ { "两独立样本率优效性设计" = "models/proportion/independent/superiority.md" }, { "相关系数" = "models/correlation/inequality.md" } ] }, - { "API Reference" = "api.md" } + { "API Reference" = "api.md" }, + { "Theory Reference" = "theory.md" } ] site_name = "pystatpower" site_url = "https://pystatpower.readthedocs.io"