cond_indep_normal_nonlinear¶

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

Conditionally independent normal distributions. Example 3 from 1.

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

X_1, Y_1, Z &\sim N(0, 1) \\
Z_1 &= 0.5 \left( \frac{Z^3}{7} + \frac{Z}{2} \right) \\
Z_2 &= \frac{Z^3}{2} + \frac{Z}{3} \\
X_2 &= Z_1 + \tanh(X_1) \\
X &= X_2 + \frac{X_2^3}{3}\\
Y_2 &= Z_2 + Y_1 \\
Y &= Y_2 + \frac{Y_2^3}{3}

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.

cond_indep_lognormal

cond_indep_binomial