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Vavilov.cxx
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1 // @(#)root/mathmore:$Id$
2 // Authors: B. List 29.4.2010
3 
4 
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25 
26 // Implementation file for class Vavilov
27 //
28 // Created by: blist at Thu Apr 29 11:19:00 2010
29 //
30 // Last update: Thu Apr 29 11:19:00 2010
31 //
32 
33 
34 #include "Math/Vavilov.h"
35 #include "Math/VavilovAccurate.h"
36 #include "Math/SpecFuncMathCore.h"
37 #include "Math/SpecFuncMathMore.h"
38 
39 #include <cmath>
40 
41 namespace ROOT {
42 namespace Math {
43 
44 static const double eu = 0.577215664901532860606; // Euler's constant
45 
47 {
48 }
49 
51 {
52  // desctructor (clean up resources)
53 }
54 
55 
56 double Vavilov::Mode() const {
57  double x = -4.22784335098467134e-01-std::log(GetKappa())-GetBeta2();
58  if (x>-0.223172) x = -0.223172;
59  double eps = 0.01;
60  double dx;
61 
62  do {
63  double p0 = Pdf (x - eps);
64  double p1 = Pdf (x);
65  double p2 = Pdf (x + eps);
66  double y1 = 0.5*(p2-p0)/eps;
67  double y2 = (p2-2*p1+p0)/(eps*eps);
68  dx = - y1/y2;
69  x += dx;
70  if (fabs(dx) < eps) eps = 0.1*fabs(dx);
71  } while (fabs(dx) > 1E-5);
72  return x;
73 }
74 
75 double Vavilov::Mode(double kappa, double beta2) {
76  SetKappaBeta2 (kappa, beta2);
77  return Mode();
78 }
79 
80 double Vavilov::Mean() const {
81  return Mean (GetKappa(), GetBeta2());
82 }
83 
84 double Vavilov::Mean(double kappa, double beta2) {
85  return eu-1-std::log(kappa)-beta2;
86 }
87 
88 double Vavilov::Variance() const {
89  return Variance (GetKappa(), GetBeta2());
90 }
91 
92 double Vavilov::Variance(double kappa, double beta2) {
93  return (1-0.5*beta2)/kappa;
94 }
95 
96 double Vavilov::Skewness() const {
97  return Skewness (GetKappa(), GetBeta2());
98 }
99 
100 double Vavilov::Skewness(double kappa, double beta2) {
101  return (0.5-beta2/3)/(kappa*kappa) * std::pow ((1-0.5*beta2)/kappa, -1.5);
102 }
103 
104 
105 double Vavilov::Kurtosis() const {
106  return Kurtosis (GetKappa(), GetBeta2());
107 }
108 
109 double Vavilov::Kurtosis(double kappa, double beta2) {
110  return (1./3-0.25*beta2)*pow (1-0.5*beta2, -2)/kappa;
111 }
112 
113 
114 } // namespace Math
115 } // namespace ROOT
log
double log(double)
x
Double_t x[n]
Definition: legend1.C:17
SpecFuncMathMore.h
ROOT::Math::Vavilov::Pdf
virtual double Pdf(double x) const =0
Evaluate the Vavilov probability density function.
SpecFuncMathCore.h
ROOT::Math::Vavilov::~Vavilov
virtual ~Vavilov()
Destructor.
Definition: Vavilov.cxx:88
ROOT::Math::Vavilov::Vavilov
Vavilov()
Default constructor.
Definition: Vavilov.cxx:84
ROOT::Math::fabs
VecExpr< UnaryOp< Fabs< T >, VecExpr< A, T, D >, T >, T, D > fabs(const VecExpr< A, T, D > &rhs)
Definition: UnaryOperators.h:131
ROOT::Math::Vavilov::Skewness
virtual double Skewness() const
Return the theoretical skewness .
Definition: Vavilov.cxx:134
ROOT::Math::Vavilov::Kurtosis
virtual double Kurtosis() const
Return the theoretical kurtosis .
Definition: Vavilov.cxx:143
ROOT::Math::Vavilov::Mode
virtual double Mode() const
Return the value of where the pdf is maximal.
Definition: Vavilov.cxx:94
ROOT::Math::eu
static const double eu
Definition: Vavilov.cxx:82
ROOT::Math::Vavilov::GetBeta2
virtual double GetBeta2() const =0
Return the current value of .
ROOT::Math::Vavilov::Mean
virtual double Mean() const
Return the theoretical mean , where is Euler's constant.
Definition: Vavilov.cxx:118
VavilovAccurate.h
Vavilov.h
ROOT::Math::Vavilov::SetKappaBeta2
virtual void SetKappaBeta2(double kappa, double beta2)=0
Change and and recalculate coefficients if necessary.
ROOT::Math::Vavilov::GetKappa
virtual double GetKappa() const =0
Return the current value of .
pow
double pow(double, double)
ROOT
VSD Structures.
Definition: StringConv.hxx:21
TMath::E
constexpr Double_t E()
Base of natural log:
Definition: TMath.h:102
Math
ROOT::Math::Vavilov::Variance
virtual double Variance() const
Return the theoretical variance .
Definition: Vavilov.cxx:126