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Thousand feet of the station from the base soil. - Lao Tzu.

 

Foreword

To give the base soil (to understand intuitively) statistics of.

Mean mean

E(X)=\bar{X}= \frac{\sum_{i=1}^{n} {X_i}}{n}

Standard deviation standard deviation

\sqrt{D(x)}=\sqrt{ \frac{\sum_{i=1}^{n} \left({X_i-\bar X} \right ) ^2}{n}}

(Flat) variance variance

var(X)=D(X)=\frac{\sum_{i=1}^{n} \left({X_i-\bar X} \right ) ^2}{n}

 

Covariance representation

Variance and standard deviation of one-dimensional random variables described degree of scatter, the variance modeled defined, to give

Covariance covariance

cov(X,Y)=\frac{\sum_{i=1}^{n} \left({X_i-\bar X} \right ) \left({Y_i-\bar Y} \right ) }{n}

covariance represents the relationship between two random variables. (English directly represent the importance ...)

covariance demonstrated no correlation is 0, then n is a positive correlation, vice versa.

 

The correlation coefficient

XY correlation coefficient expressed as a direct \large \rho _{XY}, values between -1-1, irrelevant if compared with 0, vice versa.

\large \rho _{XY}=\frac{cov(X,Y)}{\sqrt{D(X) }\sqrt{D(Y) }}

 

covariance matrix

covariance of the n-dimensional random variable   \large C_{ij}=cov(X_i,Y_j) \qquad (i,j=1,2,\cdots,n )  are present,

covariance matrix as follows:

\large \boldsymbol{C}=\begin{vmatrix} C_{11 }& \cdots &C_{1n } \\ \vdots& & \vdots \\ C_{n1 }& \cdots & C_{nn } \end{vmatrix}

 

for example:

Two-dimensional random variable \large (X_1,X_2) \sim N(\mu _1,\mu _2,\delta _1^2,\delta_2^2,\rho ), which  \large \rho  is the correlation coefficient.

The covariance matrix as follows

 \large \boldsymbol{C}=\begin{pmatrix} C_{11} &C_{12} \\ C_{21} & C_{22} \end{pmatrix} =\begin{pmatrix} D(X_1) &cov(X_1,X_2) \\ cov(X_2,X_1) & D(X_2) \end{pmatrix} = \begin{pmatrix}\delta_1^2 &\rho \delta_1 \delta_2 \\ \rho \delta_1 \delta_2 & \delta_2^2 \end{pmatrix}

 

 

 

 

 

 

 

 

 

 

 

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Origin blog.csdn.net/Bluenapa/article/details/102521233