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 71 of file VavilovAccurateQuantile.h.

Public Member Functions
	VavilovAccurateQuantile ()
	Default constructor. More...

	VavilovAccurateQuantile (const double *p)
	Constructor with parameter values. More...

virtual	~VavilovAccurateQuantile ()
	Destructor. More...

virtual IBaseFunctionOneDim *	Clone () const
	Return a clone of the object. More...

virtual double	DoEval (double x) const
	Evaluate the function. More...

virtual double	DoEvalPar (double x, const double *p) const
	Evaluate the function, using parameters p. More...

virtual unsigned int	NPar () const
	Return the number of Parameters. More...

virtual std::string	ParameterName (unsigned int i) const
	Return the name of the i-th parameter (starting from zero) More...

virtual const double *	Parameters () const
	Access the parameter values. More...

virtual void	SetParameters (const double *p)
	Set the parameter values. More...

Public Member Functions inherited from ROOT::Math::IParametricFunctionOneDim
double	operator() (double x, const double *p) const
	Evaluate function at a point x and for given parameters p. More...

double	operator() (const double x, const double p) const
	multidim-like interface More...

Public Member Functions inherited from ROOT::Math::IBaseFunctionOneDim
	IBaseFunctionOneDim ()

virtual	~IBaseFunctionOneDim ()
	virtual destructor More...

double	operator() (double x) const
	Evaluate the function at a point x Use the a pure virtual private method DoEval which must be implemented by sub-classes. More...

double	operator() (const double *x) const
	Evaluate the function at a point x[]. More...

Public Member Functions inherited from ROOT::Math::IBaseParam
virtual	~IBaseParam ()
	Virtual Destructor (no operations) More...

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