# dcor.partial_distance_covariance¶

partial_distance_covariance(x, y, z)[source]

Partial distance covariance estimator.

Compute the estimator for the partial distance covariance of the random vectors corresponding to $$x$$ and $$y$$ with respect to the random variable corresponding to $$z$$.

Parameters
• x (array_like) – First random vector. The columns correspond with the individual random variables while the rows are individual instances of the random vector.

• y (array_like) – Second random vector. The columns correspond with the individual random variables while the rows are individual instances of the random vector.

• z (array_like) – Random vector with respect to which the partial distance covariance is computed. The columns correspond with the individual random variables while the rows are individual instances of the random vector.

Returns

Value of the estimator of the partial distance covariance.

Return type

numpy scalar

Examples

>>> import numpy as np
>>> import dcor
>>> a = np.array([[1, 2, 3, 4],
...               [5, 6, 7, 8],
...               [9, 10, 11, 12],
...               [13, 14, 15, 16]])
>>> b = np.array([[1], [0], [0], [1]])
>>> c = np.array([[1, 3, 4],
...               [5, 7, 8],
...               [9, 11, 15],
...               [13, 15, 16]])
>>> dcor.partial_distance_covariance(a, a, c)
0.0024298...
>>> dcor.partial_distance_covariance(a, b, c)
0.0347030...
>>> dcor.partial_distance_covariance(b, b, c)
0.4956241...