Bicop.pdf_deriv2

Bicop.pdf_deriv2(self, u: numpy.ndarray, deriv: str, parameters: numpy.ndarray | None = None, num_threads: int = 1) → numpy.ndarray

Evaluates a second derivative of the copula density.

deriv combines two first-order components, e.g. "par1par1", "par1u1", "u1u2"; a single component means differentiating twice.

Notes

If parameters is given, the copula is evaluated with a different parameter set per row of u instead of the stored parameters. parameters is then an (n, p) array with one row per row of u and p == len(self.parameters) columns, in the family’s natural (unrotated) parameterization, and the evaluation may be parallelized over num_threads. This is supported for parametric families only; a nonparametric family, a wrong shape, or non-finite or out-of-bounds values raise RuntimeError.