Bicop.fit

Bicop.fit(self: pyvinecopulib.Bicop, data: numpy.ndarray[numpy.float64[m, n]], controls: pyvinecopulib.FitControlsBicop = FitControlsBicop()) → None

Fits a bivariate copula (with fixed family) to data.

For parametric models, two different methods are available. "mle" fits the parameters by maximum-likelihood. "itau" uses inversion of Kendall’s \(\tau\), but is only available for one-parameter families and the Student t copula. For the latter, there is a one-to-one transformation for the first parameter, the second is found by profile likelihood optimization (with accuracy of at least 0.5). Nonparametric families have specialized methods, no specification is required.

When at least one variable is discrete, two types of “observations” are required: the first \(n \times 2\) block contains realizations of \(F_{X_1}(X_1), F_{X_2}(X_2)\). Let \(k\) denote the number of discrete variables (either one or two). Then the second \(n \times k\) block contains realizations of \(F_{X_k}(X_k^-)\). The minus indicates a left-sided limit of the cdf. For continuous variables the left limit and the cdf itself coincide. For, e.g., an integer-valued variable, it holds \(F_{X_k}(X_k^-) = F_{X_k}(X_k - 1)\).

Parameter data:

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

Parameter controls:

The controls (see FitControlsBicop).