vinecopulas.bivariate
Created on Thu Feb 22 16:39:03 2024
Attributes
Functions
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Fits a specific copula to data. |
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Fits the best copula to data based on a selected list of copulas to fit to using the AIC. |
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Generates random numbers from a chosen copula with specific parameters. |
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Generates conditional random numbers from a chosen copula with specific parameters. |
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Computes the cumulative distribution function. |
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Computes the probability density function. |
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Computes the h-function (conditional CDF) of a copula with respect to variable u1 or u2. |
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Computes the inverse h-function (inverse conditional CDF) of a copula with respect to variable u1 or u2. |
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Computes the negative likelihood function. |
Module Contents
- vinecopulas.bivariate.fit(cop, u)[source]
Fits a specific copula to data.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1).
u : A 2-d numpy array containing the samples for which the copulae will be fit. Column 1 contains variable u1, and column 2 contains variable u2.
- Returns:
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
- vinecopulas.bivariate.bestcop(cops, u)[source]
Fits the best copula to data based on a selected list of copulas to fit to using the AIC.
- Arguments:
cops : A list of integers referring to the copulae of interest for which the fit has to be evaluated. eg. a list of [1, 10] refers to the Gaussian and Frank copula (see Table 1).
u : A 2-d numpy array containing the samples for which the copulae will be fit and evaluated. Column 1 contains variable u1, and column 2 contains variable u2.
- Returns:
cop : An integer referring to the copula with the best fit. eg. a 1 refers to the gaussian copula (see Table 1).
par : The correlation parameters of the copula with the best fit, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
aic : The Akaike information criterion of the copula with the best fit.
- vinecopulas.bivariate.random(cop, par, n)[source]
Generates random numbers from a chosen copula with specific parameters.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1).
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
n : Number of random samples to return, specified a positive integer.
- Returns:
u : A 2-d numpy array containing random samples with n amount of rows. Column 1 contains variable u1, and column 2 contains variable u2.
- vinecopulas.bivariate.randomconditional(cop, ui, par, n, un=1)[source]
Generates conditional random numbers from a chosen copula with specific parameters.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1)
ui : A 1-d numpy array containing the samples of variable u1, if evaluated with respect to u1, or u2 if evaluated with respect to u2 on which conditional samples should be computed
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1)
n: number of samples to draw
un : indicated with respect to which variable the conditional samples have to be drawn. if un = 1, conditional samples of u2 will be drawn based on u1, if un = 2, conditional samples of u1 will be drawn based on u2.
- Returns:
uii : A 1-d numpy array containing the inverse h-function of the copula evaluated with respect to u1 or u2.
- vinecopulas.bivariate.CDF(cop, u, par)[source]
Computes the cumulative distribution function.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1).
u : A 2-d numpy array containing the samples for which the CDF will be calculated. Column 1 contains variable u1, and column 2 contains variable u2.
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
- Returns:
p : A 1-d numpy array containing the cumulative distribution function of the copula evaluated at u1 and u2.
- vinecopulas.bivariate.PDF(cop, u, par)[source]
Computes the probability density function.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1).
u : A 2-d numpy array containing the samples for which the PDF will be calculated. Column 1 contains variable u1, and column 2 contains variable u2.
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
- Returns:
y : A 1-d numpy array containing the probability density function of the copula evaluated at u1 and u2.
- vinecopulas.bivariate.hfunc(cop, u1, u2, par, un=1)[source]
Computes the h-function (conditional CDF) of a copula with respect to variable u1 or u2.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1)
u1 : A 1-d numpy array containing the samples of variable u1
u2 : A 1-d numpy array containing the samples of variable u2
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
un : indicated with respect to which variable the h-function has to be calculated. if un = 1, the h-function is calculated with respect to u1 (c(u2|u1)), if un = 2, the h-function is calculated with respect to u2 (c(u1|u2)).
- Returns:
y : A 1-d numpy array containing the h-function of the copula evaluated with respect to u1 or u2.
- vinecopulas.bivariate.hfuncinverse(cop, ui, y, par, un=1)[source]
Computes the inverse h-function (inverse conditional CDF) of a copula with respect to variable u1 or u2.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1).
ui : A 1-d numpy array containing the samples of variable u1, if evaluated with respect to u1, or u2 if evaluated with respect to u2.
y : A 1-d numpy array containing the h-function of the copula evaluated with respect to u1 or u2.
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
un : indicated with respect to which variable the h-function has to be calculated. if un = 1, the h-function is calculated with respect to u1 (c(u2|u1)), if un = 2, the h-function is calculated with respect to u2 (c(u1|u2)).
- Returns:
uii : A 1-d numpy array containing the inverse h-function of the copula evaluated with respect to u1 or u2.
- vinecopulas.bivariate.neg_likelihood(par, cop, u)[source]
Computes the negative likelihood function.
- Arguments:
cop : An integer referring to the copula of choice. eg. a 1 refers to the gaussian copula (see Table 1).
u : A 2-d numpy array containing the samples for which the CDF will be calculated. Column 1 contains variable u1, and column 2 contains variable u2.
par : The correlation parameters of the copula, provided as a scalar value for copulas with one parameter and as a list for copulas with more parameters (see Table 1).
- Returns:
l : The negative likelihood as a scalar value.