Bicop

class Bicop(*args, **kwargs)

A class for bivariate copula models.

The model is fully characterized by the family, rotation (one of 0, 90, 180, 270), a matrix of parameters, and variable types (two strings, one for each variable, either "c" for continuous or "d" for discrete).

Implemented families (see BicopFamily):

| type          | full name             | string identifier     |
|---------------|-----------------------|-----------------------|
| -             | Independence          | "indep"               |
| Elliptical    | Gaussian              | "gaussian"            |
|               | Student t             | "student"             |
| Archimedean   | Clayton               | "clayton"             |
|               | Gumbel                | "gumbel"              |
|               | Frank                 | "frank"               |
|               | Joe                   | "joe"                 |
|               | Clayton-Gumbel (BB1)  | "bb1"                 |
|               | Joe-Gumbel (BB6)      | "bb6"                 |
|               | Joe-Clayton (BB7)     | "bb7"                 |
|               | Joe-Frank (BB8)       | "bb8"                 |
| Extreme-Value | Tawn                  | "tawn"                |
| Nonparametric | Transformation kernel | "tll"                 |

Attributes:

beta: Returns ——- float Blomqvist’s beta implied by the current parameters.
family: Returns ——- BicopFamily the copula family.
nobs: Returns ——- int the number of observations used to fit the copula (0 until fit() has been called).
npars: Returns ——- float the number of parameters in the copula model.
parameters: Returns ——- ndarray, shape (n, m), dtype float the copula parameter(s) as a matrix (shape depends on the family).
parameters_lower_bounds: Gets lower bounds for copula parameters.
parameters_upper_bounds: Gets upper bounds for copula parameters.
rotation: Returns ——- int the copula rotation in degrees (one of 0, 90, 180, 270).
taildep: Returns ——- ndarray, shape (n, m), dtype float the tail dependence coefficients implied by the current parameters, as a 2x2 matrix; see parameters_to_taildep().
tau: Returns ——- float Kendall’s tau implied by the current parameters.
var_types: Returns ——- list of str the variable types of the two variables (each "c" for continuous or "d" for discrete).

Methods

`aic`(self[, u])	Evaluates the Akaike information criterion (AIC).
`bic`(self[, u])	Evaluates the Bayesian information criterion (BIC).
`cdf`(self, u[, parameters, num_threads])	Evaluates the copula distribution.
`fit`(self, data[, controls])	Fits a bivariate copula (with fixed family) to data.
`flip`(self)	Adjusts the copula model to a change in the variable order.
`from_data`(data[, controls, var_types])	Instantiates from data.
`from_family`([family, rotation, parameters, ...])	Instantiates a specific bivariate copula model.
`from_file`(filename)	Instantiates from a JSON or CBOR file.
`from_json`(json)	Instantiates from a JSON-like str object.
`gradient`(self, u[, parameters, num_threads])	Evaluates the gradient of the average log-likelihood.
`hessian`(self, u[, parameters, num_threads])	Evaluates the Hessian of the average log-likelihood.
`hessian_full`(self, u[, parameters, num_threads])	Evaluates the per-observation Hessians.
`hfunc1`(self, u[, parameters, num_threads])	Evaluates the first h-function.
`hfunc1_deriv`(self, u, deriv[, parameters, ...])	Evaluates a first derivative of the first h-function \(h_1(u_1, u_2) = P(U_2 \le u_2 \| U_1 = u_1)\).
`hfunc1_deriv2`(self, u, deriv[, parameters, ...])	Evaluates a second derivative of the first h-function.
`hfunc2`(self, u[, parameters, num_threads])	Evaluates the second h-function.
`hfunc2_deriv`(self, u, deriv[, parameters, ...])	Evaluates a first derivative of the second h-function \(h_2(u_1, u_2) = P(U_1 \le u_1 \| U_2 = u_2)\).
`hfunc2_deriv2`(self, u, deriv[, parameters, ...])	Evaluates a second derivative of the second h-function.
`hinv1`(self, u[, parameters, num_threads])	Evaluates the inverse of the first h-function.
`hinv2`(self, u[, parameters, num_threads])	Evaluates the inverse of the second h-function.
`loglik`(self[, u, parameters, num_threads])	Evaluates the log-likelihood.
`logpdf_deriv`(self, u, deriv[, parameters, ...])	Evaluates a first derivative of the log-density \(\partial \log c / \partial \cdot\).
`logpdf_deriv2`(self, u, deriv[, parameters, ...])	Evaluates a second derivative of the log-density.
`mbic`(self[, u, psi0])	Evaluates the modified Bayesian information criterion (mBIC).
`parameters_to_beta`(self, parameters)	Converts the copula parameters to Blomqvist's \(\beta\).
`parameters_to_taildep`(self, parameters)	Converts the copula parameters to the tail dependence coefficients.
`parameters_to_tau`(self, parameters)	Converts the copula parameters to Kendall's \(tau\).
`pdf`(self, u[, parameters, num_threads])	Evaluates the copula density.
`pdf_deriv`(self, u, deriv[, parameters, ...])	Evaluates a first derivative of the copula density.
`pdf_deriv2`(self, u, deriv[, parameters, ...])	Evaluates a second derivative of the copula density.
`plot`(self[, type, margin_type, xylim, grid_size])	Generates a plot for the Bicop object.
`scores`(self, u[, parameters, num_threads])	Evaluates the per-observation scores.
`scores_cov`(self, u[, parameters, num_threads])	Computes the covariance matrix of the scores.
`scores_full`(self, u[, parameters, num_threads])	Evaluates the scores, bundled in a `ScoresResult`.
`select`(self, data[, controls])	Selects the best fitting model.
`simulate`(self, n[, qrng, seeds])	Simulates from a bivariate copula.
`tau_to_parameters`(self, tau)	Converts a Kendall's \(\tau\)into copula parameters for one-parameter families.
`to_file`(self, filename)	Writes the copula object into a JSON or CBOR file.
`to_json`(self)	Convert the copula into a nlohmann::json object.

Attributes

`beta`	Returns:
`family`	Returns:
`nobs`	Returns:
`npars`	Returns:
`parameters`	Returns:
`parameters_lower_bounds`	Gets lower bounds for copula parameters.
`parameters_upper_bounds`	Gets upper bounds for copula parameters.
`rotation`	Returns:
`taildep`	Returns:
`tau`	Returns:
`var_types`	Returns:

Methods

`__init__`	Default constructor for the `Bicop` class.
`aic`	Evaluates the Akaike information criterion (AIC).
`bic`	Evaluates the Bayesian information criterion (BIC).
`cdf`	Evaluates the copula distribution.
`fit`	Fits a bivariate copula (with fixed family) to data.
`flip`	Adjusts the copula model to a change in the variable order.
`from_data`	Instantiates from data.
`from_family`	Instantiates a specific bivariate copula model.
`from_file`	Instantiates from a JSON or CBOR file.
`from_json`	Instantiates from a JSON-like str object.
`gradient`	Evaluates the gradient of the average log-likelihood.
`hessian`	Evaluates the Hessian of the average log-likelihood.
`hessian_full`	Evaluates the per-observation Hessians.
`hfunc1`	Evaluates the first h-function.
`hfunc1_deriv`	Evaluates a first derivative of the first h-function \(h_1(u_1, u_2) = P(U_2 \le u_2 \| U_1 = u_1)\).
`hfunc1_deriv2`	Evaluates a second derivative of the first h-function.
`hfunc2`	Evaluates the second h-function.
`hfunc2_deriv`	Evaluates a first derivative of the second h-function \(h_2(u_1, u_2) = P(U_1 \le u_1 \| U_2 = u_2)\).
`hfunc2_deriv2`	Evaluates a second derivative of the second h-function.
`hinv1`	Evaluates the inverse of the first h-function.
`hinv2`	Evaluates the inverse of the second h-function.
`loglik`	Evaluates the log-likelihood.
`logpdf_deriv`	Evaluates a first derivative of the log-density \(\partial \log c / \partial \cdot\).
`logpdf_deriv2`	Evaluates a second derivative of the log-density.
`mbic`	Evaluates the modified Bayesian information criterion (mBIC).
`parameters_to_beta`	Converts the copula parameters to Blomqvist's \(\beta\).
`parameters_to_taildep`	Converts the copula parameters to the tail dependence coefficients.
`parameters_to_tau`	Converts the copula parameters to Kendall's \(tau\).
`pdf`	Evaluates the copula density.
`pdf_deriv`	Evaluates a first derivative of the copula density.
`pdf_deriv2`	Evaluates a second derivative of the copula density.
`plot`	Generates a plot for the Bicop object.
`scores`	Evaluates the per-observation scores.
`scores_cov`	Computes the covariance matrix of the scores.
`scores_full`	Evaluates the scores, bundled in a `ScoresResult`.
`select`	Selects the best fitting model.
`simulate`	Simulates from a bivariate copula.
`tau_to_parameters`	Converts a Kendall's \(\tau\)into copula parameters for one-parameter families.
`to_file`	Writes the copula object into a JSON or CBOR file.
`to_json`	Convert the copula into a nlohmann::json object.