TorchBicop.cdf

TorchBicop.cdf(u, x=None)

Evaluates the bivariate copula CDF.

\[C(u_1, u_2) = \int_0^{u_1} \int_0^{u_2} c(s, t)\, ds\, dt.\]

Computed via nested trapezoidal integration when cache_integrals=False, or via a single bilinear interpolation on the precomputed cache when cache_integrals=True.

Parameters:

uTensor, shape (n, 2), dtype float

Pseudo-observations in [0, 1]^2.

xTensor or None, optional

Conditioning variables, shape (n, k). Ignored by TorchBicop (an unconditional pair copula); accepted so the class satisfies the BicopLike contract.

Returns:

Tensor, shape (n,), dtype float

CDF values in [1e-10, 1 - 1e-10].