VavilovAccurateQuantile.h

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// @(#)root/mathmore:$Id$
// Authors: B. List 29.4.2010

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  * Copyright (c) 2004 ROOT Foundation,  CERN/PH-SFT                   *
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// Header file for class VavilovAccurateQuantile
//
// Created by: blist  at Thu Apr 29 11:19:00 2010
//
// Last update: Thu Apr 29 11:19:00 2010
//
#ifndef ROOT_Math_VavilovAccurateQuantile
#define ROOT_Math_VavilovAccurateQuantile


#include "Math/IParamFunction.h"
#include "Math/VavilovAccurate.h"

namespace ROOT {
namespace Math {

//____________________________________________________________________________
/**
   Class describing the Vavilov quantile function.

   The probability density function of the Vavilov distribution
   is given by:
  \f[ p(\lambda; \kappa, \beta^2) =
  \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} \phi(s) e^{\lambda s} ds\f]
   where \f$\phi(s) = e^{C} e^{\psi(s)}\f$
   with  \f$ C = \kappa (1+\beta^2 \gamma )\f$
   and \f[\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}}\f].
   \f$ \gamma = 0.5772156649\dots\f$ is Euler's constant.

   The parameters are:
   - 0: Norm: Normalization constant
   - 1: x0:   Location parameter
   - 2: xi:   Width parameter
   - 3: kappa: Parameter \f$\kappa\f$ of the Vavilov distribution
   - 4: beta2: Parameter \f$\beta^2\f$ of the Vavilov distribution

   Benno List, June 2010


   @ingroup StatFunc
 */


class VavilovAccurateQuantile: public IParametricFunctionOneDim {
   public:

      /**
         Default constructor
      */
      VavilovAccurateQuantile();

      /**
         Constructor with parameter values
         @param p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).
      */
      VavilovAccurateQuantile(const double *p);

      /**
         Destructor
      */
      virtual ~VavilovAccurateQuantile ();

      /**
         Access the parameter values
      */
      virtual const double * Parameters() const;

      /**
         Set the parameter values
         @param p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).

      */
      virtual void SetParameters(const double * p );

      /**
         Return the number of Parameters
      */
      virtual unsigned int NPar() const;

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

      /**
         Evaluate the function

       @param x The Quantile \f$z\f$ , \f$0 \le z \le 1\f$
       */
      virtual double DoEval(double x) const;

      /**
         Evaluate the function, using parameters p

       @param x The Quantile \f$z\f$, \f$0 \le z \le 1\f$
         @param p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).
       */
      virtual double DoEvalPar(double x, const double * p) const;

      /**
         Return a clone of the object
       */
      virtual IBaseFunctionOneDim  * Clone() const;

   private:
     double fP[5];

};


} // namespace Math
} // namespace ROOT

#endif /* ROOT_Math_VavilovAccurateQuantile */