correlated_t_linear¶

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

Conditionally dependent t-distributed data with linear dependence. Example 9 from 1

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

Z_1, Z_2, \cdots, Z_p, Z_{p+1}, Z_{p+2}  &\sim t(1)\\
X &= (Z_1, Z_2, Z_{p-1}, Z_p + Z_{p+1})\\
Y &= Z_1 + Z_2 + \cdots + Z_p + Z_{p+1} + Z_{p+2}\\
Z &= Z_{p+1}

Parameters

n (int) -- The number of samples desired by the simulation (>= 5).
p (int) -- The number of dimentions for variable x.

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_lognormal

correlated_t_quadratic