Class describing the Vavilov quantile function.

The probability density function of the Vavilov distribution is given by:

\[ p(\lambda; \kappa, \beta^2) = \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} \phi(s) e^{\lambda s} ds\]

where \(\phi(s) = e^{C} e^{\psi(s)}\) with \( C = \kappa (1+\beta^2 \gamma )\) and

\[\psi(s) = s \ln \kappa + (s+\beta^2 \kappa) \cdot \left ( \int \limits_{0}^{1} \frac{1 - e^{\frac{-st}{\kappa}}}{t} \, dt- \gamma \right ) - \kappa \, e^{\frac{-s}{\kappa}}\]

. \( \gamma = 0.5772156649\dots\) is Euler's constant.

The parameters are:

0: Norm: Normalization constant
1: x0: Location parameter
2: xi: Width parameter
3: kappa: Parameter \(\kappa\) of the Vavilov distribution
4: beta2: Parameter \(\beta^2\) of the Vavilov distribution

Benno List, June 2010

Definition at line 72 of file VavilovAccurateQuantile.h.

Public Types
typedef IBaseFunctionOneDim	BaseFunc

Public Member Functions
	VavilovAccurateQuantile ()
	Default constructor.
	VavilovAccurateQuantile (const double *p)
	Constructor with parameter values.
	~VavilovAccurateQuantile () override
	Destructor.
IBaseFunctionOneDim *	Clone () const override
	Return a clone of the object.
double	Derivative (const double *x) const
	Compatibility method with multi-dimensional interface for partial derivative.
double	Derivative (double x) const
	Return the derivative of the function at a point x Use the private method DoDerivative.
double	DoEval (double x) const override
	Evaluate the function.
double	DoEvalPar (double x, const double *p) const override
	Evaluate the function, using parameters p.
void	FdF (const double x, double &f, double df) const
	Compatibility method with multi-dimensional interface for Gradient and function evaluation.
virtual void	FdF (double x, double &f, double &df) const
	Optimized method to evaluate at the same time the function value and derivative at a point x.
void	Gradient (const double x, double g) const
	Compatibility method with multi-dimensional interface for Gradient.
virtual bool	HasGradient () const
unsigned int	NPar () const override
	Return the number of Parameters.
double	operator() (const double *x) const
	Evaluate the function at a point x[].
double	operator() (const double x, const double p) const
	multidim-like interface
double	operator() (double x) const
	Evaluate the function at a point x.
double	operator() (double x, const double *p) const
	Evaluate function at a point x and for given parameters p.
std::string	ParameterName (unsigned int i) const override
	Return the name of the i-th parameter (starting from zero).
const double *	Parameters () const override
	Access the parameter values.
void	SetParameters (const double *p) override
	Set the parameter values.

Private Attributes
double	fP [5]

#include <Math/VavilovAccurateQuantile.h>

Inheritance diagram for ROOT::Math::VavilovAccurateQuantile:

Member Typedef Documentation

◆ BaseFunc

typedef IBaseFunctionOneDim ROOT::Math::IParametricFunctionOneDim::BaseFunc

inherited

Definition at line 166 of file IParamFunction.h.

Constructor & Destructor Documentation

◆ VavilovAccurateQuantile() [1/2]

ROOT::Math::VavilovAccurateQuantile::VavilovAccurateQuantile ( )

Default constructor.

Definition at line 40 of file VavilovAccurateQuantile.cxx.

◆ VavilovAccurateQuantile() [2/2]

ROOT::Math::VavilovAccurateQuantile::VavilovAccurateQuantile ( const double * p )

Constructor with parameter values.

Parameters

p	vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

Definition at line 48 of file VavilovAccurateQuantile.cxx.

◆ ~VavilovAccurateQuantile()

ROOT::Math::VavilovAccurateQuantile::~VavilovAccurateQuantile ( )

override

Destructor.

Definition at line 61 of file VavilovAccurateQuantile.cxx.

Member Function Documentation

◆ Clone()

IBaseFunctionOneDim * ROOT::Math::VavilovAccurateQuantile::Clone ( ) const

overridevirtual

Return a clone of the object.

Implements ROOT::Math::IBaseFunctionOneDim.

Definition at line 101 of file VavilovAccurateQuantile.cxx.

◆ Derivative() [1/2]

double ROOT::Math::IBaseFunctionOneDim::Derivative ( const double * x ) const

inlineinherited

Compatibility method with multi-dimensional interface for partial derivative.

Definition at line 186 of file IFunction.h.

◆ Derivative() [2/2]

double ROOT::Math::IBaseFunctionOneDim::Derivative ( double x ) const

inlineinherited

Return the derivative of the function at a point x Use the private method DoDerivative.

Definition at line 183 of file IFunction.h.

◆ DoEval()

double ROOT::Math::VavilovAccurateQuantile::DoEval ( double x ) const

overridevirtual

Evaluate the function.

Parameters

x	The Quantile \(z\) , \(0 \le z \le 1\)

Reimplemented from ROOT::Math::IParametricFunctionOneDim.

Definition at line 89 of file VavilovAccurateQuantile.cxx.

◆ DoEvalPar()

double ROOT::Math::VavilovAccurateQuantile::DoEvalPar	(	double	x,
		const double *	p ) const

overridevirtual

Evaluate the function, using parameters p.

Parameters

x	The Quantile \(z\), \(0 \le z \le 1\)
p	vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

Implements ROOT::Math::IParametricFunctionOneDim.

Definition at line 94 of file VavilovAccurateQuantile.cxx.

◆ FdF() [1/2]

void ROOT::Math::IBaseFunctionOneDim::FdF	(	const double *	x,
		double &	f,
		double *	df ) const

inlineinherited

Compatibility method with multi-dimensional interface for Gradient and function evaluation.

Definition at line 202 of file IFunction.h.

◆ FdF() [2/2]

virtual void ROOT::Math::IBaseFunctionOneDim::FdF	(	double	x,
		double &	f,
		double &	df ) const

inlinevirtualinherited

Optimized method to evaluate at the same time the function value and derivative at a point x.

Often both value and derivatives are needed and it is often more efficient to compute them at the same time. Derived class should implement this method if performances play an important role and if it is faster to evaluate value and derivative at the same time.

Reimplemented in ROOT::Math::Polynomial, and ROOT::Math::WrappedTF1.

Definition at line 195 of file IFunction.h.

◆ Gradient()

void ROOT::Math::IBaseFunctionOneDim::Gradient	(	const double *	x,
		double *	g ) const

inlineinherited

Compatibility method with multi-dimensional interface for Gradient.

Definition at line 189 of file IFunction.h.

◆ HasGradient()

virtual bool ROOT::Math::IBaseFunctionOneDim::HasGradient ( ) const

inlinevirtualinherited

Reimplemented in ROOT::Math::IGradientFunctionOneDim.

Definition at line 179 of file IFunction.h.

◆ NPar()

unsigned int ROOT::Math::VavilovAccurateQuantile::NPar ( ) const

overridevirtual

Return the number of Parameters.

Implements ROOT::Math::IBaseParam.

Definition at line 74 of file VavilovAccurateQuantile.cxx.

◆ operator()() [1/4]

double ROOT::Math::IBaseFunctionOneDim::operator() ( const double * x ) const

inlineinherited

Evaluate the function at a point x[].

Compatible method with multi-dimensional functions.

Definition at line 175 of file IFunction.h.

◆ operator()() [2/4]

double ROOT::Math::IParametricFunctionOneDim::operator()	(	const double *	x,
		const double *	p ) const

inlineinherited

multidim-like interface

Definition at line 187 of file IParamFunction.h.

◆ operator()() [3/4]

double ROOT::Math::IBaseFunctionOneDim::operator() ( double x ) const

inlineinherited

Evaluate the function at a point x.

Use the a pure virtual private method DoEval which must be implemented by sub-classes.

Definition at line 171 of file IFunction.h.

◆ operator()() [4/4]

double ROOT::Math::IParametricFunctionOneDim::operator()	(	double	x,
		const double *	p ) const

inlineinherited

Evaluate function at a point x and for given parameters p.

This method does not change the internal status of the function (internal parameter values). If for some reason one prefers caching the parameter values, SetParameters(p) and then operator()(x) should be called. Use the pure virtual function DoEvalPar to implement it

Definition at line 178 of file IParamFunction.h.

◆ ParameterName()

std::string ROOT::Math::VavilovAccurateQuantile::ParameterName ( unsigned int i ) const

overridevirtual

Return the name of the i-th parameter (starting from zero).

Reimplemented from ROOT::Math::IBaseParam.

Definition at line 78 of file VavilovAccurateQuantile.cxx.

◆ Parameters()

const double * ROOT::Math::VavilovAccurateQuantile::Parameters ( ) const

overridevirtual

Access the parameter values.

Implements ROOT::Math::IBaseParam.

Definition at line 64 of file VavilovAccurateQuantile.cxx.

◆ SetParameters()

void ROOT::Math::VavilovAccurateQuantile::SetParameters ( const double * p )

overridevirtual

Set the parameter values.

Parameters

p	vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

Implements ROOT::Math::IBaseParam.

Definition at line 68 of file VavilovAccurateQuantile.cxx.

Member Data Documentation

◆ fP

double ROOT::Math::VavilovAccurateQuantile::fP[5]

private

Definition at line 134 of file VavilovAccurateQuantile.h.

The documentation for this class was generated from the following files:

math/mathmore/inc/Math/VavilovAccurateQuantile.h
math/mathmore/src/VavilovAccurateQuantile.cxx

Public Types

Public Member Functions

Private Attributes

Member Typedef Documentation

◆ BaseFunc

Constructor & Destructor Documentation

◆ VavilovAccurateQuantile() [1/2]

◆ VavilovAccurateQuantile() [2/2]

◆ ~VavilovAccurateQuantile()

Member Function Documentation

◆ Clone()

◆ Derivative() [1/2]

◆ Derivative() [2/2]

◆ DoEval()

◆ DoEvalPar()

◆ FdF() [1/2]

◆ FdF() [2/2]

◆ Gradient()

◆ HasGradient()

◆ NPar()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ ParameterName()

◆ Parameters()

◆ SetParameters()

Member Data Documentation

◆ fP