pystra.dependence.copula.IndependentCopula#

Use it: User guide · Worked example · Theory

class IndependentCopula(dimension)[source]#

Bases: GaussianCopula

Product copula of the specified dimension.

Parameters:: dimension (int) – Positive number of independent uniform coordinates.

Methods

`cdf`	Evaluate the copula CDF, including unit-cube boundaries.
`from_kendall_tau`	Construct from rank correlations, validating the resulting shape.
`inverse_rosenblatt`	Map independent conditional uniforms to dependent marginals.
`logpdf`	Evaluate log density at interior uniform coordinates.
`pdf`	Evaluate the copula density at interior uniform coordinates.
`rosenblatt`	Map dependent uniforms to independent conditional uniforms.
`rvs`	Sample rows using a local NumPy random generator.

cdf(probabilities, **kwargs)[source]#

Evaluate the copula CDF, including unit-cube boundaries.

Parameters:

probabilities (ArrayLike) – Marginal probabilities in [0, 1], in original order.
**kwargs (Any) – Keyword arguments forwarded to SciPy’s multivariate CDF integration.

Returns:

Cumulative probability for one point or one value per row of points.

Return type:

float | ndarray

classmethod from_kendall_tau(tau, **kwargs)[source]#

Construct from rank correlations, validating the resulting shape.

Parameters:

tau (ArrayLike) – Finite Kendall rank correlations in [-1, 1]. The transformed latent matrix must be symmetric positive definite with a unit diagonal.
**kwargs (Any) – Additional subclass constructor arguments, such as df for StudentTCopula.

Returns:

An instance of the class on which this method was called.

Return type:

Self

property correlation: ndarray#: Copy of the latent correlation (shape matrix for Student-t).

inverse_rosenblatt(probabilities, order=None)#

Map independent conditional uniforms to dependent marginals.

Parameters:

probabilities (ArrayLike) – Interior independent uniforms in original column positions.
order (Sequence[int] | ndarray | None) – Conditioning permutation used by rosenblatt().

Returns:

Dependent uniform marginal coordinates, with the input shape and order.

Return type:

ndarray

property kendall_tau: ndarray#: Pairwise Kendall rank correlation implied by this elliptical copula.

logpdf(probabilities)#

Evaluate log density at interior uniform coordinates.

Parameters:: probabilities (ArrayLike) – Marginal probabilities strictly between zero and one, in original order.
Returns:: Log density for one point or one value per row of points.
Return type:: float | ndarray

pdf(probabilities)#

Evaluate the copula density at interior uniform coordinates.

Parameters:: probabilities (ArrayLike) – Marginal probabilities strictly between zero and one, in original order.
Returns:: Density for one point or one value per row of points.
Return type:: float | ndarray
Raises:: ValueError – If the coordinates have an invalid shape or lie outside the interior.

rosenblatt(probabilities, order=None)#

Map dependent uniforms to independent conditional uniforms.

Parameters:

probabilities (ArrayLike) – Interior uniform marginal coordinates in original order.
order (Sequence[int] | ndarray | None) – Conditioning permutation; the default is original marginal order.

Returns:

Conditional uniforms with the input shape. Column order[k] holds the k-th conditional innovation, so original column labels are retained.

Return type:

ndarray

Raises:

ValueError – If coordinates, conditioning order or computed probabilities are invalid.

rvs(size=1, seed=None)#

Sample rows using a local NumPy random generator.

Parameters:

size (int) – Nonnegative number of observations.
seed (int | integer | Sequence[int] | ndarray | SeedSequence | BitGenerator | Generator | None) – Input to numpy.random.default_rng. A supplied generator is reused and advances; other seeds construct a local generator.

Returns:

Uniform marginal coordinates with this copula’s dependence.

Return type:

ndarray