Статистика - формулы
Ниже приведен список формул статистики, используемых в учебных пособиях по статистике Tutorialspoint. Каждая формула связана с веб-страницей, на которой описывается, как ее использовать.
А
Adjusted R-Squared - $ {R_{adj}^2 = 1 - [\frac{(1-R^2)(n-1)}{n-k-1}]} $
Arithmetic Mean - $ \bar{x} = \frac{_{\sum {x}}}{N} $
Arithmetic Median - Медиана = значение $ \frac{N+1}{2})^{th}\ item $
Arithmetic Range - $ {Coefficient\ of\ Range = \frac{L-S}{L+S}} $
B
Best Point Estimation - $ {MLE = \frac{S}{T}} $
Binomial Distribution - $ {P(X-x)} = ^{n}{C_x}{Q^{n-x}}.{p^x} $
C
Chebyshev's Theorem - $ {1-\frac{1}{k^2}} $
Circular Permutation - $ {P_n = (n-1)!} $
Cohen's kappa coefficient - $ {k = \frac{p_0 - p_e}{1-p_e} = 1 - \frac{1-p_o}{1-p_e}} $
Combination - $ {C(n,r) = \frac{n!}{r!(n-r)!}} $
Combination with replacement - $ {^nC_r = \frac{(n+r-1)!}{r!(n-1)!} } $
Continuous Uniform Distribution - f (x) = $ \begin{cases} 1/(b-a), & \text{when $ а \ ле х \ ле б $} \\ 0, & \text{when $х \ lt а$ or $х \ gt b$} \end{cases} $
Coefficient of Variation - $ {CV = \frac{\sigma}{X} \times 100 } $
Correlation Co-efficient - $ {r = \frac{N \sum xy - (\sum x)(\sum y)}{\sqrt{[N\sum x^2 - (\sum x)^2][N\sum y^2 - (\sum y)^2]}} } $
Cumulative Poisson Distribution - $ {F(x,\lambda) = \sum_{k=0}^x \frac{e^{- \lambda} \lambda ^x}{k!}} $
D
Deciles Statistics - $ {D_i = l + \frac{h}{f}(\frac{iN}{10} - c); i = 1,2,3...,9} $
Deciles Statistics - $ {D_i = l + \frac{h}{f}(\frac{iN}{10} - c); i = 1,2,3...,9} $
F
Factorial - $ {n! = 1 \times 2 \times 3 ... \times n} $
г
Geometric Mean - $ G.M. = \sqrt[n]{x_1x_2x_3...x_n} $
Geometric Probability Distribution - $ {P(X=x) = p \times q^{x-1} } $
Grand Mean - $ {X_{GM} = \frac{\sum x}{N}} $
ЧАС
Harmonic Mean - $ H.M. = \frac{W}{\sum (\frac{W}{X})} $
Harmonic Mean - $ H.M. = \frac{W}{\sum (\frac{W}{X})} $
Hypergeometric Distribution - $ {h(x;N,n,K) = \frac{[C(k,x)][C(N-k,n-x)]}{C(N,n)}} $
я
Interval Estimation - $ {\mu = \bar x \pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt n}} $
L
Logistic Regression - $ {\pi(x) = \frac{e^{\alpha + \beta x}}{1 + e^{\alpha + \beta x}}} $
M
Mean Deviation - $ {MD} =\frac{1}{N} \sum{|X-A|} = \frac{\sum{|D|}}{N} $
Mean Difference - $ {Mean\ Difference= \frac{\sum x_1}{n} - \frac{\sum x_2}{n}} $
Multinomial Distribution - $ {P_r = \frac{n!}{(n_1!)(n_2!)...(n_x!)} {P_1}^{n_1}{P_2}^{n_2}...{P_x}^{n_x}} $
N
Negative Binomial Distribution - $ {f(x) = P(X=x) = (x-1r-1)(1-p)x-rpr} $
Normal Distribution - $ {y = \frac{1}{\sqrt {2 \pi}}e^{\frac{-(x - \mu)^2}{2 \sigma}} } $
О
One Proportion Z Test - $ { z = \frac {\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}} } $
п
Permutation - $ { {^nP_r = \frac{n!}{(n-r)!} } $
Permutation with Replacement - $ {^nP_r = n^r } $
Poisson Distribution - $ {P(X-x)} = {e^{-m}}.\frac{m^x}{x!} $
probability - $ {P(A) = \frac{Number\ of\ favourable\ cases}{Total\ number\ of\ equally\ likely\ cases} = \frac{m}{n}} $
Probability Additive Theorem - $ {P(A\ or\ B) = P(A) + P(B) \\[7pt] P (A \cup B) = P(A) + P(B)} $
Probability Multiplicative Theorem - $ {P(A\ and\ B) = P(A) \times P(B) \\[7pt] P (AB) = P(A) \times P(B)} $
Probability Bayes Theorem - $ {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)}} $
Probability Density Function - $ {P(a \le X \le b) = \int_a^b f(x) d_x} $
р
Reliability Coefficient - $ {Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ - Sum\ of\ Variance)}{Total Variance})} $
Residual Sum of Squares - $ {RSS = \sum_{i=0}^n(\epsilon_i)^2 = \sum_{i=0}^n(y_i - (\alpha + \beta x_i))^2} $
S
Shannon Wiener Diversity Index - $ { H = \sum[(p_i) \times ln(p_i)] } $
Standard Deviation - $ \sigma = \sqrt{\frac{\sum_{i=1}^n{(x-\bar x)^2}}{N-1}} $
Standard Error ( SE ) - $ SE_\bar{x} = \frac{s}{\sqrt{n}} $
Sum of Square - $ {Sum\ of\ Squares\ = \sum(x_i - \bar x)^2 } $
Т
Trimmed Mean - $ \mu = \frac{\sum {X_i}}{n} $