Bicop

class Bicop

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

family

The copula family.

nobs

The number of observations (only for fitted objects).

npars

The number of parameters (for nonparametric families, a conceptually similar definition).

parameters

The copula parameter(s).

rotation

The copula rotation.

tau

The Kendall's tau.

var_types

The type of the two variables.

Methods

__init__

Creates a new instance of the 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.

hfunc1

Evaluates the first h-function.

hfunc2

Evaluates 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.

mbic

Evaluates the modified Bayesian information criterion (mBIC).

parameters_lower_bounds

Gets lower bounds for copula parameters.

parameters_to_tau

Converts the copula parameters to Kendall's \(tau\).

parameters_upper_bounds

Gets upper bounds for copula parameters.

pdf

Evaluates the copula density.

plot

Generates a plot for the Bicop object.

select

Selects the best fitting model.

simulate

Simulates from a bivariate copula.

str

Summarizes the model into a string (can be used for printing).

tau_to_parameters

Converts a Kendall's \(\tau\) into copula parameters for one-parameter families.

to_json

Write the copula object into a JSON file.