Vavilov.cxx

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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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// Implementation file for class Vavilov
//
// Created by: blist  at Thu Apr 29 11:19:00 2010
//
// Last update: Thu Apr 29 11:19:00 2010
//


#include "Math/Vavilov.h"
#include "Math/VavilovAccurate.h"
#include "Math/SpecFuncMathCore.h"
#include "Math/SpecFuncMathMore.h"

#include <cmath>

namespace ROOT {
namespace Math {

static const double eu = 0.577215664901532860606;      // Euler's constant

Vavilov::Vavilov()
{
}

Vavilov::~Vavilov()
{
   // desctructor (clean up resources)
}


double Vavilov::Mode() const {
   double x = -4.22784335098467134e-01-std::log(GetKappa())-GetBeta2();
   if (x>-0.223172) x = -0.223172;
   double eps = 0.01;
   double dx;

   do {
      double p0 = Pdf (x - eps);
      double p1 = Pdf (x);
      double p2 = Pdf (x + eps);
      double y1 = 0.5*(p2-p0)/eps;
      double y2 = (p2-2*p1+p0)/(eps*eps);
      dx = - y1/y2;
      x += dx;
      if (fabs(dx) < eps) eps = 0.1*fabs(dx);
   } while (fabs(dx) > 1E-5);
   return x;
}

double Vavilov::Mode(double kappa, double beta2) {
   SetKappaBeta2 (kappa, beta2);
   return Mode();
}

double Vavilov::Mean() const {
   return Mean (GetKappa(), GetBeta2());
}

double Vavilov::Mean(double kappa, double beta2) {
   return eu-1-std::log(kappa)-beta2;
}

double Vavilov::Variance() const {
   return Variance (GetKappa(), GetBeta2());
}

double Vavilov::Variance(double kappa, double beta2) {
   return (1-0.5*beta2)/kappa;
}

double Vavilov::Skewness() const {
   return Skewness (GetKappa(), GetBeta2());
}

double Vavilov::Skewness(double kappa, double beta2) {
   return (0.5-beta2/3)/(kappa*kappa) * std::pow ((1-0.5*beta2)/kappa, -1.5);
}


double Vavilov::Kurtosis() const {
   return Kurtosis (GetKappa(), GetBeta2());
}

double Vavilov::Kurtosis(double kappa, double beta2) {
   return (1./3-0.25*beta2)*pow (1-0.5*beta2, -2)/kappa;
}


} // namespace Math
} // namespace ROOT