Statistics 公式
以下是 Tutorialspoint 统计教程中使用的统计公式列表。每个公式都链接到描述如何使用公式的网页。
A
调整后的 R 平方-$ {R_{adj}^2 = 1-[\frac{(1-R^2)(n-1)}{nk-1}]} $
算术平均值-$ \bar{x} = \frac{_{\sum {x}}}{ N} $
算术中位数-中位数 = $ \frac{N+1}{2})^{th} 的值\ 项目 $
算术范围-$ {Coefficient\ of\ Range = \frac{LS}{L+S}} $
B
最佳点估计-$ {MLE = \frac{S}{T}} $
二项分布-$ {P(Xx)} = ^{n}{C_x}{Q^{nx }}.{p^x} $
C
切比雪夫定理-$ {1-\frac{1}{k^2}} $
循环排列-$ {P_n = (n-1)!} $
Cohen 的 kappa 系数-$ {k = \frac{p_0-p_e}{1-p_e} = 1-\frac{1-p_o}{1-p_e}} $
组合-$ {C(n,r) = \frac{n!}{r!(nr) !}} $
替换组合-$ {^nC_r = \frac{(n+r-1)!}{r !(n-1)!} } $
连续均匀分布-f(x) = $ \begin{cases} 1/(ba), & \ text{when $ a \le x \le b $} \\ 0, & \text{when $x \lt a$ or $x \gt b$} \end{cases} $
变异系数-$ {CV = \frac{\sigma}{X} \times 100 } $
相关系数-$ {r = \frac{N \sum xy-(\sum x)( \sum y)}{\sqrt{[N\sum x^2-(\sum x)^2][N\sum y^2-(\sum y)^2]}} } $
累积泊松分布-$ {F(x,\lambda) = \sum_{k=0}^x \frac{e^{-\lambda} \lambda ^x}{k!}} $
D
Deciles 统计-$ {D_i = l + \frac{h}{f}(\frac{iN} {10}-c); i = 1,2,3...,9} $
Deciles 统计-$ {D_i = l + \frac{h}{f}(\frac{iN} {10}-c); i = 1,2,3...,9} $
F
阶乘-$ {n! = 1 \times 2 \times 3 ... \times n} $
G
几何平均值-$ G.M. = \sqrt[n]{x_1x_2x_3...x_n} $
几何概率分布-$ {P(X=x) = p \times q^{x-1} } $
均值-$ {X_{GM} = \frac{\sum x}{N}} $
H
谐波平均值-$ H.M. = \frac{W}{\sum (\frac{W}{X})} $
谐波平均值-$ H.M. = \frac{W}{\sum (\frac{W}{X})} $
超几何分布-$ {h(x;N,n,K) = \frac{[C(k) ,x)][C(Nk,nx)]}{C(N,n)}} $
我
区间估计-$ {\mu = \bar x \pm Z_{\frac{\alpha}{2 }}\frac{\sigma}{\sqrt n}} $
L
逻辑回归-$ {\pi(x) = \frac{e^{\alpha + \beta x }}{1 + e^{\alpha + \beta x}}} $
M
平均偏差-$ {MD} =\frac{1}{N} \sum{|XA|} = \frac{\sum{|D|}}{N} $
平均差-$ {Mean\ Difference= \frac{\sum x_1}{n}-\frac{ \sum x_2}{n}} $
多项分布-$ {P_r = \frac{n!}{(n_1!)(n_2!)。 ..(n_x!)} {P_1}^{n_1}{P_2}^{n_2}...{P_x}^{n_x}} $
N
负二项分布-$ {f(x) = P(X=x) = (x-1r-1)(1-p)x-rpr} $
正态分布-$ {y = \frac{1}{\sqrt {2 \pi}}e^ {\frac{-(x-\mu)^2}{2 \sigma}} } $
O
比例 Z 检验-$ { z = \frac {\hat p-p_o}{\sqrt{\压裂{p_o(1-p_o)}{n}}} } $
P
排列-$ { {^nP_r = \frac{n!}{(nr)!} } $
置换置换-$ {^nP_r = n^r } $
泊松分布-$ {P(Xx)} = {e^{-m}}.\frac{ m^x}{x!} $
概率-$ {P(A) = \frac{Number\ of\ favourable\ cases}{Total\ number\ of\equal\likely\cases} = \frac{m}{n}} $
概率可加定理-$ {P(A\ or\ B) = P(A) + P(B ) \\[7pt] P (A \cup B) = P(A) + P(B)} $
概率乘法定理-$ {P(A\ and\ B) = P(A) \times P(B) \\[7pt] P (AB) = P(A) \times P(B)} $
概率贝叶斯定理-$ {P(A_i/B) = \frac{P(A_i) \times P (B/A_i)}{\sum_{i=1}^k P(A_i) \times P (B/A_i)}} $
概率密度函数-$ {P(a \le X \le b) = \int_a^bf(x ) d_x} $
R
可靠性系数-$ {Reliability\ Coefficient,\ RC = (\frac{N}{(N-1 )}) \times (\frac{(Total\ Variance\-Sum\ of\ Variance)}{Total Variance})} $
残差平方和-$ {RSS = \sum_{i=0}^n(\epsilon_i)^ 2 = \sum_{i=0}^n(y_i-(\alpha + \beta x_i))^2} $
S
香农维纳多样性指数-$ { H = \sum[(p_i) \times ln(p_i)] } $
标准偏差-$ \sigma = \sqrt{\frac{\sum_{i=1}^n{ (x-\bar x)^2}}{N-1}} $
标准误差 (SE)-$ SE_\bar{x} = \frac{s}{\sqrt{ n}} $
平方和-$ {Sum\ of\ Squares\ = \sum(x_i-\bar x)^ 2 } $
T
修剪平均值-$ \mu = \frac{\sum {X_i}}{n} $
