Independence Copula Distribution. More...

#include <IndependenceCopula.h>

Inheritance diagram for Multivariate::IndependenceCopula:

Public Member Functions
	IndependenceCopula (unsigned int Dimension=2U)
	Constructs an Independence copula. More...

Eigen::MatrixXd	ExtractSamples (unsigned int NumSamples) const
	Generates multiple simulations from the copula. More...

double	GetCumulativeDesity (const Eigen::VectorXd &Coordinates) const
	Computes the copula function in correspondence of the supplied coordinates. More...

double	GetDensity (const Eigen::VectorXd &Coordinates) const
	Computes the copula density function in correspondence of the supplied coordinates. More...

Eigen::VectorXd	GetQuantile (double Prob) const
	Computes the inverse copula function in correspondence of the supplied probability. More...

Public Member Functions inherited from Multivariate::AbstarctCopula
Eigen::RowVectorXd	ExtractSample () const
	Generates a single simulation from the copula. More...

std::map< unsigned int, std::vector< double > >	ExtractSamplesMap (unsigned int NumSamples) const
	Generates multiple simulations from the copula. More...

std::vector< double >	ExtractSampleVector () const
	Generates a single simulation from the copula. More...

double	GetCumulativeDesity (const std::vector< double > &Coordinates) const
	Computes the copula function in correspondence of the supplied coordinates. More...

unsigned int	GetCurrentSeed () const
	Get the random number generator seed. More...

double	GetDensity (const std::vector< double > &Coordinates) const
	Computes the probability density function of the copula in correspondence of the supplied coordinates. More...

unsigned int	GetDimension () const
	Get the dimensionality of the copula. More...

std::vector< double >	GetQuantileVector (double Prob) const
	Computes the inverse copula function in correspondence of the supplied probability. More...

bool	IsValid () const
	Check if the copula is valid. More...

bool	SetDimension (unsigned int Dimension)
	Set the dimensionality of the copula. More...

void	SetRandomSeed (unsigned int NewSeed)
	Set the random number generator seed. More...

double *	GetQuantileArray (double Prob)
	Computes the inverse copula function in correspondence of the supplied probability. More...

double	GetCumulativeDesity (double *Coordinates) const
	Computes the copula function in correspondence of the supplied coordinates. More...

double	GetDensity (double *Coordinates) const
	Computes the probability density function of the copula in correspondence of the supplied coordinates. More...

double *	ExtractSampleArray () const
	Generates a single simulation from the copula. More...

double **	ExtractSamplesMatix (unsigned int NumSamples) const
	Generates a single simulation from the copula. More...

Detailed Description

Independence Copula Distribution.

This class provides the functionality of calculating the probability density value, cumulative probability density value, inverse cumulative probability density and generate random samples from an Independence copula.

Defining:

\( k \) as the dimensionality of the copula

The independence copula distribution funtion is defined as: \( C(\textbf{x})= \prod_{n=1}^k x_n \) for \( \textbf{x} \in \textbf{(0,1)} \)

This is quite a trivial copula but is supplied for completeness

If you construct multiple instances of this class, to avoid the generated samples to be the same, you should supply a different seed. To do so, for example, you can call MyDistribution.SetRandomSeed(MyDistribution.GetCurrentSeed()+1U);

Please refer to the Examples page for usage examples.

Remarks: This class is re-entrant

Date: November 2013

License: This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

Here, you can find a copy of the GNU Lesser General Public License. Alternatively, see gnu.org.

Constructor & Destructor Documentation

Multivariate::IndependenceCopula::IndependenceCopula ( unsigned int Dimension = 2U )

inline

Constructs an Independence copula.

Parameters

Dimension The dimensionality of the copula

Construct an Independence copula.

In case The Dimension less than 2 the class will be considered invalid (it can be checked using IsValid()) and won't produce any result until the problem is fixed.

If dimension is unspecified, a bivariate copula is constructed

Member Function Documentation

Eigen::MatrixXd Multivariate::IndependenceCopula::ExtractSamples ( unsigned int NumSamples ) const

inlinevirtual

Generates multiple simulations from the copula.

Parameters

NumSamples The number of simulation to run

Returns: A matrix with columns equal to the dimensionality of the distribution and rows equal to the number of simulations

This function generates NumSamples simulation from the current copula and returns them in matrix form.

If NumSamples is 0 or the copula is invalid, a null matrix is returned

Implements Multivariate::AbstarctCopula.

double Multivariate::IndependenceCopula::GetCumulativeDesity ( const Eigen::VectorXd & Coordinates ) const

inlinevirtual

Computes the copula function in correspondence of the supplied coordinates.

Parameters

Coordinates A vector containing the coordinates of the point for which the pdf should be computed

Returns: The value of the copula function

This function computes the probability density function of the current copula associated with the given coordinates.

The coordinates must all be between 0 and 1

If the number of elements in Coordinates is different from the dimensionality of the distribution or the distribution is invalid, -1 is returned

Implements Multivariate::AbstarctCopula.

double Multivariate::IndependenceCopula::GetDensity ( const Eigen::VectorXd & Coordinates ) const

inlinevirtual

Computes the copula density function in correspondence of the supplied coordinates.

Parameters

Coordinates A vector containing the coordinates of the point for which the pdf should be computed

Returns: The value of the copula density function

This function computes the probability density function of the current copula associated with the given coordinates.

The coordinates must all be between 0 and 1

If the number of elements in Coordinates is different from the dimensionality of the distribution or the distribution is invalid, -1 is returned

Implements Multivariate::AbstarctCopula.

Eigen::VectorXd Multivariate::IndependenceCopula::GetQuantile ( double Prob ) const

inlinevirtual

Computes the inverse copula function in correspondence of the supplied probability.

Parameters

Prob	The probability for which the corresponding quantile must be found

Returns: A vector containing the coordinates of the quantile in the intervall [0;1]

This function computes the inverse cumulative density function of the current distribution associated with the given probability.

The solution is unique only in the univariate case.
Generally the system of equations \( F^{-1}(Coordinates_1 \cdots Coordinates_k)=Prob \) has k-1 degrees of freedom, where k is the dimensionality of the distribution.
The additional restriction imposed to get to an unique solution is that each coordinate has equal distance from it's mean.

If the probability supplied is greater than 1, less than 0 or the distribution is invalid, an empty vector is returned.

Implements Multivariate::AbstarctCopula.

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation