# copulas.bivariate.independence module¶

class copulas.bivariate.independence.Independence(copula_type=None, random_seed=None)[source]

This class represent the copula for two independent variables.

copula_type = 3
cumulative_distribution(X)[source]

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)[source]

Fit the copula to the given data.

Parameters

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

Returns

None

generator(t)[source]

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)[source]

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)[source]

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

Parameters
• ynp.ndarray value of $$F(u|v)$$.

• vnp.ndarray given value of v.

probability_density(X)[source]

Compute the probability density for the independence copula.