Copula¶
This file contains all the classes for copula objects.
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class
copula.Copula(dim=2, name='indep')¶ Methods
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cdf(x)¶ Returns the cumulative distribution function (CDF) of the copula.
Parameters: x : numpy array (of size d)
Values to compute CDF.
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concentrationDown(x)¶ Returns the theoritical lower concentration function.
Parameters: x : float (between 0 and 0.5)
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concentrationFunction(x)¶ Returns the theoritical concentration function.
Parameters: x : float (between 0 and 1)
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concentrationUp(x)¶ Returns the theoritical upper concentration function.
Parameters: x : float (between 0.5 and 1)
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correlations(X)¶ Compute the correlations of the specified data. Only available when dimension of copula is 2.
Parameters: X : numpy array (of size n * 2)
Values to compute correlations.
Returns: kendall : float
The Kendall tau.
pearson : float
The Pearson’s R
spearman : float
The Spearman’s R
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getDimension()¶ Returns the dimension of the copula.
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kendall()¶ Returns the Kendall’s tau. Note that you should previously have computed correlations.
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pdf(x)¶ Returns the probability distribution function (PDF) of the copula.
Parameters: x : numpy array (of size d)
Values to compute PDF.
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pearson()¶ Returns the Pearson’s r. Note that you should previously have computed correlations.
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spearman()¶ Returns the Spearman’s rho. Note that you should previously have computed correlations.
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Archimedean Copulas¶
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class
copula.ArchimedeanCopula(family='clayton', dim=2)¶ Methods
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cdf(x)¶ Returns the CDF of the copula.
Parameters: x : numpy array (of size copula dimension or n * copula dimension)
Quantiles.
Returns: float
The CDF value on x.
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fit(X, method='cmle', verbose=False, theta_bounds=None, **kwargs)¶ Fit the archimedean copula with specified data.
Parameters: X : numpy array (of size n * copula dimension)
The data to fit.
method : str
The estimation method to use. Default is ‘cmle’.
verbose : bool
Output various informations during fitting process.
theta_bounds : tuple
Definition set of theta. Use this only with custom family.
**kwargs
Arguments of method. See estimation for more details.
Returns: float
The estimated parameter of the archimedean copula.
estimationData
Various data from estimation method. Often estimated hyper-parameters.
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pdf_param(x, theta)¶ Returns the PDF of the copula with the specified theta. Use this when you want to compute PDF with another parameter.
Parameters: x : numpy array (of size n * copula dimension)
Quantiles.
theta : float
The custom parameter.
Returns: float
The PDF value on x.
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Gaussian Copulas¶
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class
copula.GaussianCopula(dim=2, sigma=[[1, 0.8], [0.8, 1]])¶ Methods
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fit(X, method='cmle', verbose=True, **kwargs)¶ Fit the Gaussian copula with specified data.
Parameters: X : numpy array (of size n * copula dimension)
The data to fit.
method : str
The estimation method to use. Default is ‘cmle’.
verbose : bool
Output various informations during fitting process.
**kwargs
Arguments of method. See estimation for more details.
Returns: float
The estimated parameters of the Gaussian copula.
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setCovariance(sigma)¶ Set the covariance of the copula.
Parameters: sigma : numpy array (of size copula dimensions * copula dimension)
The definite positive covariance matrix. Note that you should check yourself if the matrix is definite positive.
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Student Copulas¶
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class
copula.StudentCopula(dim=2, df=1, sigma=[[1, 0.6], [0.6, 1]])¶ Methods
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setCovariance(sigma)¶ Set the covariance of the copula.
Parameters: sigma : numpy array (of size copula dimensions * copula dimension)
The definite positive covariance matrix. Note that you should check yourself if the matrix is definite positive.
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