copulas.bivariate.independence module

Independence module.

class copulas.bivariate.independence.Independence(*args, **kwargs)

Bases: Bivariate

This class represent the copula for two independent variables.

copula_type = 3

cumulative_distribution(X)

Compute the cumulative distribution of the independence bivariate copula is the product.

Parameters:

X (numpy.array) – Matrix of shape (n,2), whose values are in [0, 1]

Returns:

Cumulative distribution values of given input.

Return type:

numpy.array

fit(X)

Fit the copula to the given data.

Parameters:

X (numpy.array) – Probabilites in a matrix shaped (n, 2)

Returns:

None

generator(t)

Compute the generator function for the Copula.

The generator function is a function f(t), such that an archimedian copula can be defined as

C(u1, …, uN) = f(f^-1(u1), …, f^-1(uN)).

Parameters:

t (numpy.array)

Returns:

np.array

partial_derivative(X)

Compute the conditional probability of one event conditiones to the other.

In the case of the independence copula, due to C(u,v) = u*v, we have that F(u|v) = dC/du = v.

Parameters:

X()

percent_point(y, V)

Compute the inverse of conditional cumulative distribution \(F(u|v)^-1\).

Parameters:

• y – np.ndarray value of \(F(u|v)\).

• v – np.ndarray given value of v.

probability_density(X)

Compute the probability density for the independence copula.