Bicop.hfunc2

Bicop.hfunc2(self, u: numpy.ndarray[dtype=float64, shape=(*, *), order='F']) → numpy.ndarray[dtype=float64, shape=(*), order='C']

Evaluates the second h-function.

The second h-function is $h_{2} (u_{1}, u_{2}) = P (U_{1} \leq u_{1} | U_{2} = u_{2})$ .

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 the second h-function evaluated at u.