correlated_normal_nonliear¶

hyppo.tools.correlated_normal_nonliear(n, p=1, random_state=None)¶

Conditionally dependent normal distributions with nonlinear dependence. Example 7 from 1

\((X, Y, Z) \in \mathbb{R} \times \mathbb{R} \times \mathbb{R}\): .. math:

X_1, Y_1, Z, \epsilon &\sim N(0, 1) \\
Z_1 &= 0.5(Z^3/7 + Z/2) \\
Z_2 &= (Z^3/2 + Z)/3 \\
X_2 &= Z_1 + \tanh(X_1) \\
X_3 &= X_2 + X_2^3 / 3 \\
Y_2 &= Z_2 + Y_1\\
Y_3 &= Y_2 + \tanh(Y_2 / 3) \\
X &= X_3 + \cosh\epsilon \\
Y &= Y_3 + \cosh\epsilon^2

Parameters: n (int) -- The number of samples desired by the simulation (>= 5).
Returns: x,y,z (ndarray of float) -- Simulated data matrices. x, y, and z.

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.

correlated_normal

correlated_lognormal