correlated_normal¶
Conditionally dependent normal distributions. Example 5 from 1
\((X, Y, Z) \in \mathbb{R} \times \mathbb{R} \times \mathbb{R}\): .. math:
\mu &= (0, 0, 0)\\ \Sigma &= \begin{bmatrix} 1 & 0.7 & 0.6\\ 0.7 & 1 & 0.6\\ 0.6 & 0.6 & 1 \end{bmatrix}\\ (X, Y, Z) &\sim MVN(\mu, \Sigma)
The conditional covariance matrix is given by: .. math:
\Sigma(X, Y | Z) &= \begin{bmatrix} 0.64 & 0.34\\ 0.34 & 0.64 \end{bmatrix}
- Parameters
n (
int) -- The number of samples desired by the simulation (>= 5).- Returns
x,y,z (
ndarrayoffloat) -- Simulated data matrices.x,y, andz.
References
- 1
Xueqin Wang, Wenliang Pan, Wenhao Hu, Yuan Tian, and Heping Zhang. Conditional distance correlation. Journal of the American Statistical Association, 110(512):1726–1734, 2015.
