Description of the class TGenParetoDistribution. More...

#include <TGenParetoDistribution.h>

Inheritance diagram for URANIE::DataServer::TGenParetoDistribution:

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Collaboration diagram for URANIE::DataServer::TGenParetoDistribution:

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Public Member Functions
Constructor and Destructor
	TGenParetoDistribution ()
	Default constructor.

	TGenParetoDistribution (TString name)
	Constructor by name only.

	TGenParetoDistribution (TString name, Double_t mu, Double_t sigma, Double_t xi)
	Constructor by name and statistics.

	TGenParetoDistribution (URANIE::DataServer::TAttribute *att, Double_t mu, Double_t sigma, Double_t xi)
	Constructor by attribute and statistics.

virtual	~TGenParetoDistribution ()
	Default destructor.

Getters and Setters methods
Getting and setting attribute values.
virtual void	setParameterMu (Double_t mu, Bool_t recompute=kTRUE)
	Sets the location parameter.

virtual void	setParameterSigma (Double_t sigma, Bool_t recompute=kTRUE)
	Sets the scale parameter.

virtual void	setParameterXi (Double_t xi, Bool_t recompute=kTRUE)
	Sets the shape parameter.

virtual void	setParameters (Double_t mu, Double_t sigma, Double_t xi, Bool_t recompute=kTRUE)
	Sets the scale, shape and location parameters.

virtual Double_t	getParameterMu ()
	Gets the location.

virtual Double_t	getParameterSigma ()
	Gets the scale.

virtual Double_t	getParameterXi ()
	Gets the scale.

Double_t	getXiEquation (Double_t x, Double_t skewness)

Double_t	getZ (Double_t x)
	Calculates the $\frac{x-\mu}{\sigma}$ value.

Statistical methods
The statistical methods ( pdf, cdf, quantile, ...).
virtual void	computeTheoreticalInformation ()
	Computes the theoretical values of various statistical measures, like mean, standard deviation, mode, etc.

virtual Double_t	getPDF (Double_t x)
	Returns the probability density for the value x.

virtual Double_t	getCDF (Double_t x)
	Returns the cumulative distribution for the value x.

virtual Double_t	getInvCDF (Double_t p)
	Returns the value corresponding to the cumulative density p.

Printing Log
virtual void	printLog (Option_t *option="")

Public Member Functions inherited from URANIE::DataServer::TInfiniteDistribution
	TInfiniteDistribution ()
	Default Constructor.

	TInfiniteDistribution (TString str)
	Constructor setting the name.

	TInfiniteDistribution (TString str, ELawType value)
	Constructor setting the name and the law type.

	TInfiniteDistribution (TAttribute *object, ELawType value)
	Construction of a TInfiniteDistribution from an existing TAttribute object.

virtual	~TInfiniteDistribution ()
	Default Destructor.

virtual void	setLowerBound (Double_t val)
	Sets the lower bound of the attribute.

virtual void	setUpperBound (Double_t val)
	Sets the upper bound of the attribute.

virtual void	setBounds (Double_t lower, Double_t upper)
	Sets the lower and upper bounds of the attribute.

virtual void	printLog ()
	Display information specific to this class.

Public Member Functions inherited from URANIE::DataServer::TStochasticAttribute
	TStochasticAttribute ()
	Default Constructor.

	TStochasticAttribute (TString str)
	Constructor setting the name.

	TStochasticAttribute (TString str, ELawType value)
	Constructor setting the name and the law type.

	TStochasticAttribute (TString str, ELawType value, Double_t min, Double_t max)
	Constructor setting the name, the law type, and the range (lower and upper bounds)

	TStochasticAttribute (TAttribute *object, ELawType value)
	Construction of a TStochasticAttribute from an existing TAttribute object.

virtual	~TStochasticAttribute ()
	Default Destructor.

double	getPDFforTF1 (double *x)

double	getCDFforTF1 (double *x)

double	getInvCDFforTF1 (double *x)

virtual Double_t	getTheoreticalMean ()
	Returns the theoretical value of the mean.

virtual Double_t	getTheoreticalStdDev ()
	Returns the theoretical value of the standard deviation.

virtual Double_t	getTheoreticalMode ()
	Returns the theoretical value of the mode.

void	setLawType (ELawType value)
	Sets the law type from an integer value.

void	setLawType (TString name)
	Sets the law type from a law name.

int	getLawType ()
	Returns the law type as an integer.

void	setStochasticBasis (EStochasticBasis n)
	Defines an orthogonal polynomial family to represent the stochastic attribute.

void	setDefaultStochasticBasis ()
	Sets the default orthogonal polynomial family representing the stochastic attribute.

EStochasticBasis	getStochasticBasis () const
	Returns the orthogonal polynomial which is used to represent the attribute.

virtual Double_t	getPMin ()
	Returns the minimum value of the cumulative distribution function.

virtual Double_t	getPMax ()
	Returns the maximum value of the cumulative distribution function.

Public Member Functions inherited from URANIE::DataServer::TAttribute
	TAttribute ()
	Default constructor.

	TAttribute (const char name, const char title)

	TAttribute (TString name)
	Constructor by name only.

	TAttribute (TString name, EType type)
	Constructor by name and type only.

	TAttribute (TString name, TString value, EType type)
	Constructor by name and range.

	TAttribute (TString name, Double_t lower, Double_t upper)
	Constructor by name and range.

	TAttribute (const TAttribute &attr)
	Copy constructor.

TAttribute *	Clone (const char *newname) const
	Clone an attribute with a new name.

virtual	~TAttribute ()
	Default destructor.

void	checkSizeBeforePush (const char *type, int iel, Double_t val)
	Internal method used to check the validity of all setters when dealing with vectors.

Double_t	checkSizeBeforeGet (const char *type, int iel=0)
	Internal method used to check the validity of all getters when dealing with vectors and return the request.

void	setQuantile (double prob, double quantile, int iel=0)
	Set the quantile value.

void	getQuantilesSize (int &nb, int iel=0)
	Returns the number of quantile computed and stored for element iel.

void	getQuantiles (double prob, double quantile, int iel=0)
	Returns all the probabilities and corresponding quantiles computed for element iel.

void	getQuantile (double &prob, double &quantile, int iel=0)
	Returns the value of the quantile for element iel, given the probability.

void	getQuantileVector (double &prob, vector< double > &quantile)
	Returns the vector of quantile given the probability.

Double_t	getMinimum (int iel=0)

Double_t	getMinimumSize ()
	Returns the size of the vector of minimum.

Bool_t	hasDefault ()
	Details whether this attribute has a default value.

void	setMinimum (Double_t val, int iel=0)
	Set the minimum value oef element iel.

Double_t	getMaximum (int iel=0)

Double_t	getMaximumSize ()
	Returns the size of the vector of maximum.

void	setMaximum (Double_t val, int iel=0)
	Set the maximum value oef element iel.

void	getStatisticalVector (const char *type, vector< double > &vec)
	Returns the vector of considered statistical value.

Double_t	getMean (int iel=0)

Double_t	getMeanSize ()
	Returns the size of the vector of mean.

void	setMean (Double_t val, int iel=0)
	Set the mean value oef element iel.

Double_t	getStd (int iel=0)

Double_t	getStdSize ()
	Returns the size of the vector of std.

void	setStd (Double_t val, int iel=0)
	Set the std value oef element iel.

void	setSlurmOption (TString value)

EType	getDataType () const
	Returns the datatype of the considered attribute.

TString	getDataTypeStr ()
	Returns the datatype as TString.

void	setTitle (const char *title)
	Defines the title of the attribute.

void	setTitle (TString str)

TString	getTitle ()

void	setDataType (EType thetype)
	Change the type of data.

void	setDataType (TString name)
	Change the type of data.

TString	getLegend ()
	Returns the legend of the attribut.

TString	getUnit ()

void	setUnit (TString str)

TString	getUnity ()

void	setUnity (TString str)

TString	getNote ()

void	setNote (TString str)

Bool_t	setDefault (TString value)

TString	getDefault (TString format="%e")

Bool_t	setDefaultValue (Double_t val)

Bool_t	getDefaultValue (Double_t &val)

Bool_t	hasDefaultValue ()

Bool_t	setDefaultVector (vector< double > &vec)

Bool_t	getDefaultVector (vector< double > *val)

Bool_t	hasDefaultVector ()

Bool_t	setDefaultString (TString str)

Bool_t	getDefaultString (string &str)

Bool_t	hasDefaultString ()

void	setStepValue (Double_t val)

Bool_t	getStepValue (Double_t &val)

TString	getSlurmOption ()

EOrigin	getOrigin ()

void	setOrigin (EOrigin ind)

Int_t	getShare ()

void	setOutput ()
	Sets the attribute as an output attribute.

void	setInput ()
	Sets the attribute as Input.

EAttribute	getInputOutput ()
	Returns the input/Output information of the attribute.

void	setFileNameOfKey (TString str)
	Sets the file name for a key.

list< URANIE::DataServer::TAttributeFileKey * >	getKeyList ()
	Gets KeyList for the attribute.

void	setFieldOfKey (Int_t ind)
	Sets index ind in the unique field related to a unique key.

void	setFieldOfKey (Int_t sIndex, Int_t ind)

void	setFileKey (TString sfile, TString skey="", TString sformatToSubstitute="%e", TAttributeFileKey::EFileType FileType=TAttributeFileKey::kKey)
	Defines the input files and eventually others informations like key, format to substitute.

void	setFileFlag (TString sfile, TString skey="", TString sformatToSubstitute="%e")
	Defines the input files as in the "flag" format and eventually others informations like key, format to substitute.

void	setFileXMLAttribute (TString sfile, TString sXPathAttribute, TString sformatToSubstitute="%e")
	Defines the input files as an "XML" input file with XPath attribute format and eventually the format to substitute.

void	setFileXMLField (TString sfile, TString sXPathField, TString sformatToSubstitute="%e")
	Defines the input files as an "XML" input file with XPath field and eventually the format to substitute.

void	setFileFMU (TString sfile, TString sXPathField, TString sformatToSubstitute="%e")

const char *	getFormatToSubstitute ()
	Returns the format of substitution.

void	setFormatToSubstitute (TString str)
	Sets the format of substitution.

Bool_t	isInput ()
	Tests if the attribute is an input attribute.

Bool_t	isOutput ()
	Tests if the attribute is an output attribute.

void	addShare ()

void	delShare ()

void	initShare ()

void	clearVectors ()

virtual void	setLowerBound (Double_t val, bool internalcall=false)
	Sets the lower bound value of the attribute.

Double_t	getLowerBound ()
	Gets the lower bound value of the attribute.

Bool_t	isLowerBounded ()
	Returns a boolean if the attribute have a lower bound.

virtual void	setUpperBound (Double_t val, bool internalcall=false)
	Sets the upper bound value of the attribute.

Double_t	getUpperBound ()
	Gets the upper bound value of the attribute.

Bool_t	isUpperBounded ()
	Returns a boolean if the attribute have an upper bound.

Bool_t	isBounded ()
	Returns a boolean if the attribute have a lower AND an upper bounds.

void	setLog ()

void	unsetLog ()

void	changeLog ()

Bool_t	getLog ()

TAttribute *	getSonAttribute ()

void	setSonAttribute (TAttribute *tatt)

void	removeSonAttribute ()

Int_t	getLevel ()

void	setLevel (Int_t nlevel)

Bool_t	haveSon ()

Protected Attributes
Double_t	_dparameterXi
	The shape parameter $\xi$

Double_t	_dparameterMu
	The location parameter $\mu$ .

Double_t	_dparameterSigma
	The scale parameter $\sigma$ .

TList *	_listOfInputAttributes

Protected Attributes inherited from URANIE::DataServer::TStochasticAttribute
ELawType	_lawType
	The law type ELawType.

Double_t	_dtheoreticalMean
	The theoretical mean.

Double_t	_dtheoreticalStdDev
	The theoretical standard deviation.

Double_t	_dtheoreticalMode
	The theoretical mode.

Double_t	_pmin
	The min value of cumulative density function.

Double_t	_pmax
	The max value of cumulative density function.

EStochasticBasis	_nStochasticBasis
	The stochastic representation of an orthogonal basis.

Protected Attributes inherited from URANIE::DataServer::TAttribute
TString	_sunity
	Unity.

TString	_snote
	Note.

Bool_t	_blog
	Log printing.

Int_t	_nshare
	The number of time this attribute is shared in TDataServer.

TAttribute *	_attSon
	Son attribute.

Int_t	_nlevel
	level to its "father"

Bool_t	_haveSon
	true if the attribute have a son

TString	_sFormatSubstitute
	Format to substitute the value.

list< TEventList * >	_nfields
	List of all TEventLists created for the attribute.

list< TAttributeFileKey * >	_KeyList
	List of Keys Attributes structures.

Double_t	upperBound
	Upper bound.

Bool_t	_bHaveUpperBound
	If have an upper bound.

Double_t	lowerBound
	Lower bound.

Bool_t	_bHaveLowerBound
	If have a lower bound.

Double_t	_defaultValue
	Default value.

Bool_t	_bHaveDefaultValue
	If have a default value.

vector< double >	_defaultVector
	Default value for vector.

Bool_t	_bHaveDefaultVector
	If have a default value for vector.

string	_defaultString
	Default value for string.

Bool_t	_bHaveDefaultString
	If have a default value for string.

Double_t	_stepValue
	Step value when using in Optimization.

Bool_t	_bHaveStepValue
	If have a step value.

vector< Double_t >	_vminimum
	All minimun calculated.

vector< Double_t >	_vmaximum
	All maximun calculated.

vector< Double_t >	_vmean
	All mean calculated.

vector< Double_t >	_vstd
	All std calculated.

vector< Double_t > *	_vbuffer

vector< map< double, double > * >	_vquantile
	‍buffer pointer to check addresses

EOrigin	_norigin
	The origin of the attribute (Internal of uranie, attribute or Input, Output...)

EAttribute	_nAttribute
	The nature of attributes : kInput (default) or kOutput.

EType	_nType
	The type of attribute: real (double), vector (of double), string...

TString	_slurmValue

Additional Inherited Members
Public Types inherited from URANIE::DataServer::TStochasticAttribute
enum	ELawType { kUniform , kLogUniform , kNormal , kStudent , kLogNormal , kTrapezium , kTriangular , kLogTriangular , kExponential , kBeta , kGamma , kInvGamma , kCauchy , kUniformByParts , kWeibull , kGumbel , kMultinomial , kGenPareto , kGeneralizedNormal , kGeneralizedNormalV2 , kCompose , kUnknown }
	The list of laws that a TStochasticAttribute can follow. More...

enum	EStochasticBasis { kUnknownBasis , kHermite , kLegendre , kLaguerre , kJacobi }
	The list of orthogonal polynomial families that can represent a given TStochasticAttribute. More...

Public Types inherited from URANIE::DataServer::TAttribute
enum	EOrigin { kInternal , kIterator , kConstant , kAttribute , kDeleted }

enum	EAttribute { kInput , kOutput }

enum	EType { kDefault , kReal , kVector , kString , kCategory , kInconnu }

Detailed Description

Description of the class TGenParetoDistribution.

This class defines a stochastic attribute following a Generalized Pareto Distribution (GPD).

It is specified by three parameters: location $\mu$ , scale $\sigma$ (strictly positive), and shape $\xi$ .

Probability Density Function (PDF):

$f(x) =\frac{1}{\sigma}(1 + \xi(\frac{x-\mu}{\sigma}))^{-(1/\xi +1)}$

Cumulative Distribution Function (CDF):

$F_{(\xi,\mu,\sigma)}(x) = \begin{cases}1 - \left(1+ \frac{\xi(x-\mu)}{\sigma}\right)^{-1/\xi} \,\: \xi \neq 0, \\ 1 - \exp \left(-\frac{x-\mu}{\sigma}\right) \:\: \xi = 0.\end{cases}$

Inverse CDF:

$f(p) =\frac{((1-p)^{-\xi}-1)\delta}{\xi}+\mu$

For the details about estimation of the parameters see:

J. R. M. Hosking and J. R. Wallis. Parameter and Quantile Estimation for the Generalized Pareto Distribution Source: Technometrics, Vol. 29, No. 3 (Aug., 1987), pp. 339-349

Scott D. Grimshaw. Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution Source: Technometrics, Vol. 35, No. 2 (May, 1993), pp. 185-191

V. P. SINGH & H. GUO. Parameter estimation for 3-parameter generalized pareto distribution by the principle of maximum entropy (POME) Hydrological Sciences -Journal- des Sciences Hydrologiques Vol. 40, No. 2(April, 1995), pp. 165 - 181.

Constructor & Destructor Documentation

◆ TGenParetoDistribution() [1/4]

URANIE::DataServer::TGenParetoDistribution::TGenParetoDistribution ( )

Default constructor.

Referenced by ClassImp().

◆ TGenParetoDistribution() [2/4]

URANIE::DataServer::TGenParetoDistribution::TGenParetoDistribution ( TString name )

Constructor by name only.

Parameters

name	(TString) Name of the attribute

◆ TGenParetoDistribution() [3/4]

URANIE::DataServer::TGenParetoDistribution::TGenParetoDistribution	(	TString	name,
		Double_t	mu,
		Double_t	sigma,
		Double_t	xi
	)

Constructor by name and statistics.

Parameters

name	(TString) Name of the attribute
mu	(Double_t) location parameter.
sigma	(Double_t) scale parameter (sigma > 0).
xi	(Double_t) shape parameter.

◆ TGenParetoDistribution() [4/4]

URANIE::DataServer::TGenParetoDistribution::TGenParetoDistribution	(	URANIE::DataServer::TAttribute *	att,
		Double_t	mu,
		Double_t	sigma,
		Double_t	xi
	)

Constructor by attribute and statistics.

Parameters

att	(URANIE::DataServer::TAttribute*) pointer to attribute
mu	(Double_t) location parameter.
sigma	(Double_t) scale parameter (sigma > 0).
xi	(Double_t) shape parameter.

◆ ~TGenParetoDistribution()

virtual URANIE::DataServer::TGenParetoDistribution::~TGenParetoDistribution ( )

virtual

Default destructor.

Referenced by ClassImp().

Member Function Documentation

◆ computeTheoreticalInformation()

virtual void URANIE::DataServer::TGenParetoDistribution::computeTheoreticalInformation ( )

virtual

Computes the theoretical values of various statistical measures, like mean, standard deviation, mode, etc.

Implements URANIE::DataServer::TStochasticAttribute.

Referenced by ClassImp().

◆ getCDF()

virtual Double_t URANIE::DataServer::TGenParetoDistribution::getCDF ( Double_t x )

virtual

Returns the cumulative distribution for the value x.

Parameters

x	(Double_t) An acceptable value for the attribute

Implements URANIE::DataServer::TStochasticAttribute.

Referenced by ClassImp().

◆ getInvCDF()

virtual Double_t URANIE::DataServer::TGenParetoDistribution::getInvCDF ( Double_t p )

virtual

Returns the value corresponding to the cumulative density p.

Parameters

p	(Double_t) A valid probability

Exceptions

UErrorExceptions if p is outside of the interval [0,1]

Implements URANIE::DataServer::TStochasticAttribute.

Referenced by ClassImp().

◆ getParameterMu()

virtual Double_t URANIE::DataServer::TGenParetoDistribution::getParameterMu ( )

virtual

Gets the location.

Referenced by ClassImp().

◆ getParameterSigma()

virtual Double_t URANIE::DataServer::TGenParetoDistribution::getParameterSigma ( )

virtual

Gets the scale.

Referenced by ClassImp().

◆ getParameterXi()

virtual Double_t URANIE::DataServer::TGenParetoDistribution::getParameterXi ( )

virtual

Gets the scale.

Referenced by ClassImp().

◆ getPDF()

virtual Double_t URANIE::DataServer::TGenParetoDistribution::getPDF ( Double_t x )

virtual

Returns the probability density for the value x.

Parameters

x	(Double_t) An acceptable value for the attribute

Implements URANIE::DataServer::TStochasticAttribute.

Referenced by ClassImp().

◆ getXiEquation()

Double_t URANIE::DataServer::TGenParetoDistribution::getXiEquation	(	Double_t	x,
		Double_t	skewness
	)

Defines equation to estimate the Xi parameter. Used by the Method of Moments.

Referenced by ClassImp().

◆ getZ()

Double_t URANIE::DataServer::TGenParetoDistribution::getZ ( Double_t x )

Calculates the $\frac{x-\mu}{\sigma}$ value.

Exceptions

UErrorExceptions if case if GPD is not defined for the provided x value.

Referenced by ClassImp().

◆ printLog()

virtual void URANIE::DataServer::TGenParetoDistribution::printLog ( Option_t * option = "" )

virtual

◆ setParameterMu()

virtual void URANIE::DataServer::TGenParetoDistribution::setParameterMu	(	Double_t	mu,
		Bool_t	recompute = `kTRUE`
	)

virtual

Sets the location parameter.

Referenced by ClassImp().

◆ setParameters()

virtual void URANIE::DataServer::TGenParetoDistribution::setParameters	(	Double_t	mu,
		Double_t	sigma,
		Double_t	xi,
		Bool_t	recompute = `kTRUE`
	)

virtual

Sets the scale, shape and location parameters.

Referenced by ClassImp().

◆ setParameterSigma()

virtual void URANIE::DataServer::TGenParetoDistribution::setParameterSigma	(	Double_t	sigma,
		Bool_t	recompute = `kTRUE`
	)

virtual

Sets the scale parameter.

Referenced by ClassImp().

◆ setParameterXi()

virtual void URANIE::DataServer::TGenParetoDistribution::setParameterXi	(	Double_t	xi,
		Bool_t	recompute = `kTRUE`
	)

virtual

Sets the shape parameter.

Referenced by ClassImp().

Member Data Documentation

◆ _dparameterMu

Double_t URANIE::DataServer::TGenParetoDistribution::_dparameterMu

protected

The location parameter $\mu$ .

Referenced by ClassImp().

◆ _dparameterSigma

Double_t URANIE::DataServer::TGenParetoDistribution::_dparameterSigma

protected

The scale parameter $\sigma$ .

Referenced by ClassImp().

◆ _dparameterXi

Double_t URANIE::DataServer::TGenParetoDistribution::_dparameterXi

protected

The shape parameter $\xi$

Referenced by ClassImp().

◆ _listOfInputAttributes

TList* URANIE::DataServer::TGenParetoDistribution::_listOfInputAttributes

protected

Documentation / Developer's manual

Available modules

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TGenParetoDistribution() [1/4]

◆ TGenParetoDistribution() [2/4]

◆ TGenParetoDistribution() [3/4]

◆ TGenParetoDistribution() [4/4]

◆ ~TGenParetoDistribution()

Member Function Documentation

◆ computeTheoreticalInformation()

◆ getCDF()

◆ getInvCDF()

◆ getParameterMu()

◆ getParameterSigma()

◆ getParameterXi()

◆ getPDF()

◆ getXiEquation()

◆ getZ()

◆ printLog()

◆ setParameterMu()

◆ setParameters()

◆ setParameterSigma()

◆ setParameterXi()

Member Data Documentation

◆ _dparameterMu

◆ _dparameterSigma

◆ _dparameterXi

◆ _listOfInputAttributes