[apps/probability] Define the Student distribution

apps/probability/Makefile

@@ -23,6 +23,7 @@ app_probability_src = $(addprefix apps/probability/,\
   law/exponential_law.cpp \
   law/normal_law.cpp \
   law/poisson_law.cpp \
+  law/student_law.cpp \
   law/two_parameter_law.cpp \
   law/uniform_law.cpp \
   law_controller.cpp \

apps/probability/base.de.i18n

@@ -6,12 +6,14 @@ Uniforme = "Uniform"
 Normal = "Normal"
 Poisson = "Poisson"
 ChiSquared = "Chi-Quadrat"
+Student = "Student"
 BinomialLaw = "Binomialverteilung"
 UniformLaw = "Uniformverteilung"
 ExponentialLaw = "Exponentialverteilung"
 NormalLaw = "Normalverteilung"
 PoissonLaw = "Poisson-Verteilung"
 ChiSquaredLaw = "Chi-Quadrat-Verteilung"
+StudentLaw = "Student-Verteilung"
 ChooseParameters = "Parameter auswählen"
 RepetitionNumber = "n: Anzahl der Versuche"
 SuccessProbability = "p: Erfolgswahrscheinlichkeit"

apps/probability/base.en.i18n

@@ -6,12 +6,14 @@ Uniforme = "Uniform"
 Normal = "Normal"
 Poisson = "Poisson"
 ChiSquared = "Chi-squared"
+Student = "Student"
 BinomialLaw = "Binomial distribution"
 UniformLaw = "Uniform distribution"
 ExponentialLaw = "Exponential distribution"
 NormalLaw = "Normal distribution"
 PoissonLaw = "Poisson distribution"
 ChiSquaredLaw = "Chi-squared distribution"
+StudentLaw = "Student's distribution"
 ChooseParameters = "Choose parameters"
 RepetitionNumber = "n: Number of trials"
 SuccessProbability = "p: Success probability"

apps/probability/base.es.i18n

@@ -6,12 +6,14 @@ Uniforme = "Uniforme"
 Normal = "Normal"
 Poisson = "Poisson"
 ChiSquared = "Chi-cuadrado"
+Student = "Student"
 BinomialLaw = "Distribución binomial"
 UniformLaw = "Distribución uniforme"
 ExponentialLaw = "Distribución exponencial"
 NormalLaw = "Distribución normal"
 PoissonLaw = "Distribución de Poisson"
 ChiSquaredLaw = "Distribución chi-cuadrado"
+StudentLaw = "Distribución de Student"
 ChooseParameters = "Seleccionar parámetros"
 RepetitionNumber = "n : Número de ensayos "
 SuccessProbability = "p : Probabilidad de éxito "

apps/probability/base.fr.i18n

@@ -6,12 +6,14 @@ Uniforme = "Uniforme"
 Normal = "Normale"
 Poisson = "Poisson"
 ChiSquared = "Chi2"
+Student = "Student"
 BinomialLaw = "Loi binomiale"
 UniformLaw = "Loi uniforme"
 ExponentialLaw = "Loi exponentielle"
 NormalLaw = "Loi normale"
 PoissonLaw = "Loi de Poisson"
 ChiSquaredLaw = "Loi du chi2"
+StudentLaw = "Loi de Student"
 ChooseParameters = "Choisir les paramètres"
 RepetitionNumber = "n : Nombre de répétitions"
 SuccessProbability = "p : Probabilité de succès"

apps/probability/base.pt.i18n

@@ -6,12 +6,14 @@ Uniforme = "Uniforme"
 Normal = "Normal"
 Poisson = "Poisson"
 ChiSquared = "Qui-quadrado"
+Student = "Student"
 BinomialLaw = "Distribuição binomial"
 UniformLaw = "Distribuição uniforme"
 ExponentialLaw = "Distribuição exponencial"
 NormalLaw = "Distribuição normal"
 PoissonLaw = "Distribuição de Poisson"
 ChiSquaredLaw = "Distribuição qui-quadrado"
+StudentLaw = "Distribuição de Student"
 ChooseParameters = "Selecionar os parâmetros"
 RepetitionNumber = "n : Número de ensaios"
 SuccessProbability = "p : Probabilidade de sucesso"

apps/probability/law/law.h

@@ -17,7 +17,8 @@ public:
     Exponential,
     Normal,
     Poisson,
-    ChiSquared
+    ChiSquared,
+    Student
   };
   virtual ~Law() = default;
   virtual I18n::Message title() = 0;

apps/probability/law/student_law.cpp

@@ -0,0 +1,50 @@
+#include "student_law.h"
+#include <cmath>
+#include <float.h>
+
+namespace Probability {
+
+float StudentLaw::xMin() const {
+  return -xMax();
+}
+
+float StudentLaw::xMax() const {
+  return 5.0f;
+}
+
+float StudentLaw::yMax() const {
+  return coefficient() * (1.0f + k_displayTopMarginRatio);
+}
+
+float StudentLaw::evaluateAtAbscissa(float x) const {
+  const float d = m_parameter1;
+  return coefficient() * std::pow(1+std::pow(x,2)/d, -(d+1)/2);
+}
+
+bool StudentLaw::authorizedValueAtIndex(float x, int index) const {
+  return x >= FLT_EPSILON;
+}
+
+double StudentLaw::cumulativeDistributiveFunctionAtAbscissa(double x) const {
+  return 0;
+  //TODO
+}
+
+double StudentLaw::cumulativeDistributiveInverseForProbability(double * probability) {
+  if (*probability >= 1.0) {
+    return INFINITY;
+  }
+  if (*probability <= 0.0) {
+    return -INFINITY;
+  }
+  return 0;
+  //TODO
+}
+
+float StudentLaw::coefficient() const {
+  const float d = m_parameter1;
+  const float lnOfResult = std::lgamma((d+1)/2) - std::lgamma(d/2) - (M_PI+d)/2;
+  return std::exp(lnOfResult);
+}
+
+}

apps/probability/law/student_law.h

@@ -0,0 +1,35 @@
+#ifndef PROBABILITY_STUDENT_LAW_H
+#define PROBABILITY_STUDENT_LAW_H
+
+#include "one_parameter_law.h"
+
+namespace Probability {
+
+class StudentLaw : public OneParameterLaw {
+public:
+  StudentLaw() : OneParameterLaw(4.0f) {}
+  I18n::Message title() override { return I18n::Message::StudentLaw; }
+  Type type() const override { return Type::Student; }
+  bool isContinuous() const override { return true; }
+  float xMin() const override;
+  float xMax() const override;
+  float yMax() const override;
+  I18n::Message parameterNameAtIndex(int index) override {
+    assert(index == 0);
+    return I18n::Message::D;
+  }
+  I18n::Message parameterDefinitionAtIndex(int index) override {
+    assert(index == 0);
+    return I18n::Message::DegreesOfFreedomDefinition;
+  }
+  float evaluateAtAbscissa(float x) const override;
+  bool authorizedValueAtIndex(float x, int index) const override;
+  double cumulativeDistributiveFunctionAtAbscissa(double x) const override;
+  double cumulativeDistributiveInverseForProbability(double * probability) override;
+private:
+  float coefficient() const;
+};
+
+}
+
+#endif