Bicop.pdf

Bicop.pdf(self, u: numpy.ndarray[dtype=float64, shape=(*, *), order='F']) → numpy.ndarray[dtype=float64, shape=(*), order='C']

Evaluates the copula density.

The copula density is defined as joint density divided by marginal densities, irrespective of variable types.

When at least one variable is discrete, more than two columns are required for u: the first \(n \times 2\) block contains realizations of \((F_{X_1}(x_1), F_{X_2}(x_2))\). The second \(n \times 2\) block contains realizations of \((F_{X_1}(x_1^-), F_{X_2}(x_2^-))\). The minus indicates a left-sided limit of the cdf. For, e.g., an integer-valued variable, it holds \(F_{X_1}(x_1^-) = F_{X_1}(x_1 - 1)\). For continuous variables the left limit and the cdf itself coincide. Respective columns can be omitted in the second block.

Parameters:

u – An \(n \times (2 + k)\) matrix of observations contained in \((0, 1)\), where \(k\) is the number of discrete variables.

Returns:

A length n vector of copula densities evaluated at u.