URANIE::Sampler::TPlackettCopula Class Reference

Description of the class TPlackettCopula. More...

#include <TPlackettCopula.h>

Inheritance diagram for URANIE::Sampler::TPlackettCopula:

Collaboration diagram for URANIE::Sampler::TPlackettCopula:

Public Member Functions
Constructor and Destructor
	TPlackettCopula (URANIE::DataServer::TDataServer *tds, Double_t dparam, Int_t nCalcul)
	Default constructor. More...
virtual	~TPlackettCopula ()
	Default destructor. More...
Generation of the sample
void	generateUMatrix (Option_t *option)
	Generates the matrix of U. More...
Printing Log
virtual void	printLog (Option_t *option="")
	Prints the log. More...
Public Member Functions inherited from URANIE::Sampler::TArchimedianCopula
	TArchimedianCopula (URANIE::DataServer::TDataServer *tds, Double_t dparam, Int_t nCalcul)
	Default constructor. More...
virtual	~TArchimedianCopula ()
	Default destructor. More...
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. More...
virtual	~TCopula ()
	Default destructor. More...
void	generateSample (Option_t *option="")
	Generates the sample. More...
Public Member Functions inherited from URANIE::Sampler::TSamplerStochastic
	TSamplerStochastic (URANIE::DataServer::TDataServer *tds, Option_t *option, Int_t nCalcul)
	Constructor with a dataserver. More...
virtual	~TSamplerStochastic ()
	Default destructor. More...
void	setSeed (Int_t ind=0)
	Init the seed. More...
Int_t	getSeed ()
	Returns the seed value. More...
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. More...
virtual	~TSampler ()
	Default destructor. More...
Int_t	GetID ()
	Returns the ID of the class. More...
void	setMethodName (TString str)
	Sets the method name in a global variable. More...
TString	getMethodName ()
	Gets the method name. More...
virtual URANIE::DataServer::TDataServer *	getTDS ()
	Return the TDS filling by the sampling algorithm. More...
void	parseOption (Option_t *option)
	Parse the option. More...
virtual void	createListOfAttributes ()
	Creates the List of attributes to simulate. More...
virtual void	createTuple ()
	Creates the TDSNtupleD of data with only the TStochasticAttributes. More...
URANIE::DataServer::TDSNtupleD *	getTuple ()
	Returns the TDSNtupleD of data. More...
virtual void	fillOtherAttributes ()
	Fills the TDSNtupleD of data with other TFormulaAttributes. More...
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 More...
Public Attributes inherited from URANIE::Sampler::TCopula
TMatrixD	_matUValue
	The matrix of U values. More...
Public Attributes inherited from URANIE::Sampler::TSampler
Int_t	_nS
	The size of the sample. More...
Int_t	_nX
	The size of attributes to sample. More...
URANIE::DataServer::TDSNtupleD *	_ntsample
	the tntuple of data More...
TString	_sMethod
	The title of the sampler method. More...
Bool_t	_blog
	Log Printing. More...
Bool_t	_bupdateFile
	Update the back up file when generating the attributeformula if there is some. More...
URANIE::DataServer::TDataServer *	_tds
	Pointer to a TDS. More...
TList *	_lstOfAttributesToSample
	The list of Stochastic Attributes to sample. More...
Protected Member Functions inherited from URANIE::Sampler::TSamplerStochastic
virtual void	init ()
	The preprocessing step. More...
virtual void	terminate ()
	The post-processing step. More...
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 \( (u,v)\) from a Plackett distribution with parameter \( \theta > 0\).

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

Constructor & Destructor Documentation

TPlackettCopula()

URANIE::Sampler::TPlackettCopula::TPlackettCopula	(	URANIE::DataServer::TDataServer *	tds,
		Double_t	dparam,
		Int_t	nCalcul
	)

Default constructor.

Referenced by ClassImp().

~TPlackettCopula()

virtual URANIE::Sampler::TPlackettCopula::~TPlackettCopula ( )

virtual

Default destructor.

Referenced by ClassImp().

Member Function Documentation

generateUMatrix()

void URANIE::Sampler::TPlackettCopula::generateUMatrix ( Option_t *  option )

virtual

Generates the matrix of U.

Parameters

option

(Option_t *) The option to pass.

Implements URANIE::Sampler::TCopula.

Referenced by ClassImp().

printLog()

virtual void URANIE::Sampler::TPlackettCopula::printLog ( Option_t *  option = "" )

virtual

Prints the log.

Reimplemented from URANIE::Sampler::TArchimedianCopula.

Referenced by ClassImp().