def partial_derivative(self, X):
r"""Compute partial derivative of cumulative distribution.
The partial derivative of the copula(CDF) is the conditional CDF.
_ORIGINAL: .. math:: **F(v|u) = \frac{\partial C(u,v)}{\partial u}**_
_CORRECTED.. math:: **F(u|v) = \frac{\partial C(u,v)}{\partial v}**_
The base class provides a finite difference approximation of the
partial derivative of the CDF with respect to u.
Args:
X(np.ndarray)
y(float)
Returns:
np.ndarray
"""
delta = 0.0001 * (-2 * (X[:, 1] > 0.5) + 1)
X_prime = X.copy()
X_prime[:, 1] += delta
f = self.cumulative_distribution(X)
f_prime = self.cumulative_distribution(X_prime)
return (f_prime - f) / delta