Bicop.hfunc1

Bicop.hfunc1(self: pyvinecopulib.Bicop, u: numpy.ndarray[numpy.float64[m, n]]) → numpy.ndarray[numpy.float64[m, 1]]

Evaluates the first h-function.

The first h-function is \(h_1(u_1, u_2) = P(U_2 \le u_2 | U_1 = u_1)\).

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 \((F_{X_1}(x_1^-), F_{X_1}(x_1^-))\). 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 first h-function evaluated at u.