root/Math/VavilovAccurateQuantile.h

0001 // @(#)root/mathmore:$Id$
0002 // Authors: B. List 29.4.2010
0003
0004  /**********************************************************************
0005   *                                                                    *
0006   * Copyright (c) 2004 ROOT Foundation,  CERN/PH-SFT                   *
0007   *                                                                    *
0008   * This library is free software; you can redistribute it and/or      *
0009   * modify it under the terms of the GNU General Public License        *
0010   * as published by the Free Software Foundation; either version 2     *
0011   * of the License, or (at your option) any later version.             *
0012   *                                                                    *
0013   * This library is distributed in the hope that it will be useful,    *
0014   * but WITHOUT ANY WARRANTY; without even the implied warranty of     *
0015   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU   *
0016   * General Public License for more details.                           *
0017   *                                                                    *
0018   * You should have received a copy of the GNU General Public License  *
0019   * along with this library (see file COPYING); if not, write          *
0020   * to the Free Software Foundation, Inc., 59 Temple Place, Suite      *
0021   * 330, Boston, MA 02111-1307 USA, or contact the author.             *
0022   *                                                                    *
0023   **********************************************************************/
0024
0025 // Header file for class VavilovAccurateQuantile
0026 //
0027 // Created by: blist  at Thu Apr 29 11:19:00 2010
0028 //
0029 // Last update: Thu Apr 29 11:19:00 2010
0030 //
0031 #ifndef ROOT_Math_VavilovAccurateQuantile
0032 #define ROOT_Math_VavilovAccurateQuantile
0033
0034 #include "Math/IParamFunction.h"
0035 #include "Math/VavilovAccurate.h"
0036
0037 #include <string>
0038
0039 namespace ROOT {
0040 namespace Math {
0041
0042 //____________________________________________________________________________
0043 /**
0044    Class describing the Vavilov quantile function.
0045
0046    The probability density function of the Vavilov distribution
0047    is given by:
0048   \f[ p(\lambda; \kappa, \beta^2) =
0049   \frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} \phi(s) e^{\lambda s} ds\f]
0050    where \f$\phi(s) = e^{C} e^{\psi(s)}\f$
0051    with  \f$ C = \kappa (1+\beta^2 \gamma )\f$
0052    and \f[\psi(s) = s \ln \kappa + (s+\beta^2 \kappa)
0053                \cdot \left ( \int \limits_{0}^{1}
0054                \frac{1 - e^{\frac{-st}{\kappa}}}{t} \, dt- \gamma \right )
0055                - \kappa \, e^{\frac{-s}{\kappa}}\f].
0056    \f$ \gamma = 0.5772156649\dots\f$ is Euler's constant.
0057
0058    The parameters are:
0059    - 0: Norm: Normalization constant
0060    - 1: x0:   Location parameter
0061    - 2: xi:   Width parameter
0062    - 3: kappa: Parameter \f$\kappa\f$ of the Vavilov distribution
0063    - 4: beta2: Parameter \f$\beta^2\f$ of the Vavilov distribution
0064
0065    Benno List, June 2010
0066
0067
0068    @ingroup StatFunc
0069  */
0070
0071
0072 class VavilovAccurateQuantile: public IParametricFunctionOneDim {
0073    public:
0074
0075       /**
0076          Default constructor
0077       */
0078       VavilovAccurateQuantile();
0079
0080       /**
0081          Constructor with parameter values
0082          @param p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).
0083       */
0084       VavilovAccurateQuantile(const double *p);
0085
0086       /**
0087          Destructor
0088       */
0089       ~VavilovAccurateQuantile () override;
0090
0091       /**
0092          Access the parameter values
0093       */
0094       const double * Parameters() const override;
0095
0096       /**
0097          Set the parameter values
0098          @param p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).
0099
0100       */
0101       void SetParameters(const double * p ) override;
0102
0103       /**
0104          Return the number of Parameters
0105       */
0106       unsigned int NPar() const override;
0107
0108       /**
0109          Return the name of the i-th parameter (starting from zero)
0110        */
0111       std::string ParameterName(unsigned int i) const override;
0112
0113       /**
0114          Evaluate the function
0115
0116        @param x The Quantile \f$z\f$ , \f$0 \le z \le 1\f$
0117        */
0118       double DoEval(double x) const override;
0119
0120       /**
0121          Evaluate the function, using parameters p
0122
0123        @param x The Quantile \f$z\f$, \f$0 \le z \le 1\f$
0124          @param p vector of doubles containing the parameter values (Norm, x0, xi, kappa, beta2).
0125        */
0126       double DoEvalPar(double x, const double * p) const override;
0127
0128       /**
0129          Return a clone of the object
0130        */
0131       IBaseFunctionOneDim  * Clone() const override;
0132
0133    private:
0134      double fP[5];
0135
0136 };
0137
0138
0139 } // namespace Math
0140 } // namespace ROOT
0141
0142 #endif /* ROOT_Math_VavilovAccurateQuantile */