correlated_t_nonlinear¶

hyppo.tools.correlated_t_nonlinear(n, p=4, random_state=None)¶

Conditionally dependent t-distributed data with nonlinear dependence. Example 11 from 1

\((X, Y, Z) \in \mathbb{R}^4 \times \mathbb{R}^2 \times \mathbb{R}^2\): .. math:

Z_1, \ldots, Z_4 &\sim t(2)\\
Y_1 &= \sin(Z_1) + \cos(Z_2) + Z_3^2 + Z_4^2\\
Y_2 &= Z_1^2 + Z_2^2 + Z_3 + Z_4\\
X &= (Z_1, Z_2, Z_3, Z_4)\\
Y &= (Y_1, Y_2)\\
Z &= (Z_1, Z_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_t_quadratic

condi_indep_sim