ROOT::Math::VavilovAccurateQuantile Class Reference

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 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	DoEval (double x) const override
	Evaluate the function.
double	DoEvalPar (double x, const double *p) const override
	Evaluate the function, using parameters p.
unsigned int	NPar () const override
	Return the number of Parameters.
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.
Public Member Functions inherited from ROOT::Math::IParametricFunctionOneDim
double	operator() (const double *x, const double *p) const
	multidim-like interface
double	operator() (double x, const double *p) const
	Evaluate function at a point x and for given parameters p.
Public Member Functions inherited from ROOT::Math::IBaseFunctionOneDim
virtual	~IBaseFunctionOneDim ()=default
virtual bool	HasGradient () const
double	operator() (const double *x) const
	Evaluate the function at a point x[].
double	operator() (double x) const
	Evaluate the function at a point x.
Public Member Functions inherited from ROOT::Math::IBaseParam
virtual	~IBaseParam ()
	Virtual Destructor (no operations)

Private Attributes
double	fP [5]

Additional Inherited Members
Public Types inherited from ROOT::Math::IParametricFunctionOneDim
typedef IBaseFunctionOneDim	BaseFunc
Public Types inherited from ROOT::Math::IBaseFunctionOneDim
typedef IBaseFunctionOneDim	BaseFunc

#include <Math/VavilovAccurateQuantile.h>

Inheritance diagram for ROOT::Math::VavilovAccurateQuantile:

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.

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.

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.

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.

Libraries for ROOT::Math::VavilovAccurateQuantile:

---

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

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