Description of the class TPlackettCopula. More...

#include <TPlackettCopula.h>

Inheritance diagram for URANIE::Sampler::TPlackettCopula:

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Collaboration diagram for URANIE::Sampler::TPlackettCopula:

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Public Member Functions
Constructor and Destructor
	TPlackettCopula (URANIE::DataServer::TDataServer *tds, Double_t dparam, Int_t nCalcul)
	Default constructor.

virtual	~TPlackettCopula ()
	Default destructor.

Generation of the sample
void	generateUMatrix (Option_t *option)
	Generates the matrix of U.

Printing Log
virtual void	printLog (Option_t *option="")
	Prints the log.

Public Member Functions inherited from URANIE::Sampler::TArchimedianCopula
	TArchimedianCopula (URANIE::DataServer::TDataServer *tds, Double_t dparam, Int_t nCalcul)
	Default constructor.

virtual	~TArchimedianCopula ()
	Default destructor.

Public Member Functions inherited from URANIE::Sampler::TCopula
	TCopula (URANIE::DataServer::TDataServer tds, Option_t option, Int_t nCalcul)
	Constructor with a TDataServer, the options and the size of the sample.

virtual	~TCopula ()
	Default destructor.

void	generateSample (Option_t *option="")
	Generates the sample.

Public Member Functions inherited from URANIE::Sampler::TSamplerStochastic
	TSamplerStochastic (URANIE::DataServer::TDataServer tds, Option_t option, Int_t nCalcul)
	Constructor with a dataserver.

virtual	~TSamplerStochastic ()
	Default destructor.

void	setSeed (Int_t ind=0)
	Init the seed.

Int_t	getSeed ()
	Returns the seed value.

Public Member Functions inherited from URANIE::Sampler::TSampler
	TSampler (URANIE::DataServer::TDataServer tds, Option_t option, Int_t nCalcul)
	Constructor with a TDataServer, the options and the size of the sample.

virtual	~TSampler ()
	Default destructor.

Int_t	GetID ()
	Returns the ID of the class.

void	setMethodName (TString str)
	Sets the method name in a global variable.

TString	getMethodName ()
	Gets the method name.

virtual URANIE::DataServer::TDataServer *	getTDS ()
	Return the TDS filling by the sampling algorithm.

void	parseOption (Option_t *option)
	Parse the option.

virtual void	createListOfAttributes ()
	Creates the List of attributes to simulate.

virtual void	createTuple ()
	Creates the TDSNtupleD of data with only the TStochasticAttributes.

URANIE::DataServer::TDSNtupleD *	getTuple ()
	Returns the TDSNtupleD of data.

virtual void	fillOtherAttributes ()
	Fills the TDSNtupleD of data with other TFormulaAttributes.

void	setLog ()

void	unsetLog ()

void	changeLog ()

Bool_t	getLog ()

Additional Inherited Members
Public Attributes inherited from URANIE::Sampler::TArchimedianCopula
Double_t	_dparam
	the parameter of the archimediam copula

Public Attributes inherited from URANIE::Sampler::TCopula
TMatrixD	_matUValue
	The matrix of U values

Public Attributes inherited from URANIE::Sampler::TSampler
Int_t	_nS
	The size of the sample.

Int_t	_nX
	The size of attributes to sample.

URANIE::DataServer::TDSNtupleD *	_ntsample
	the tntuple of data

TString	_sMethod
	The title of the sampler method.

Bool_t	_blog
	Log Printing.

Bool_t	_bupdateFile
	Update the back up file when generating the attributeformula if there is some.

URANIE::DataServer::TDataServer *	_tds
	Pointer to a TDS.

TList *	_lstOfAttributesToSample
	The list of Stochastic Attributes to sample.

Protected Member Functions inherited from URANIE::Sampler::TSamplerStochastic
virtual void	init ()
	The preprocessing step.

virtual void	terminate ()
	The post-processing step.

Protected Attributes inherited from URANIE::Sampler::TSamplerStochastic
Int_t	_nSeed

Detailed Description

Description of the class TPlackettCopula.

The Plackett copula for bivariate is defined by the formula

$C(u_1, u_2 ; \theta) \: = \: \frac{\left( [ 1 + (\theta - 1)(u_1+u_2)] - \sqrt{[1+(\theta - 1)(u_1+u_2)]^2 - 4 uv\theta(\theta-1)}\right)}{2(\theta-1)} \: , \: \theta > 0, \theta \neq 1$

and

$C(u_1, u_2 ; \theta) \: = \: u_1 u_2 \:, \: \theta = 1.0$

with $\theta \in [0, \infty]$ .

Implementation

We use the Johnson algorithm (1986) to generate random variates

from a Plackett distribution with parameter

.

Generate two independent uniform variate $(u,t) \in (0,1)$
Set
$b = \theta + a(\theta-1)^2$
$c = 2a(u\theta^2 + 1 - u) + \theta(1 - 2a)$
$d = \sqrt{\theta}\sqrt{\theta + 4au(1 - u)(1 - \theta)^2}$
$v = \frac{c-(1-2t)d}{2b}$
the desired pair is