GeneralizedBetaDistribution Class

[SerializableAttribute]
public class GeneralizedBetaDistribution : UnivariateContinuousDistribution, 
	ISampleableDistribution<double>, IDistribution<double>, IDistribution, 
	ICloneable, IRandomNumberGenerator<double>, IFittableDistribution<double, GeneralizedBetaOptions>, 
	IFittable<double, GeneralizedBetaOptions>, IFittable<double>, 
	IFittableDistribution<double>

<SerializableAttribute>
Public Class GeneralizedBetaDistribution
	Inherits UnivariateContinuousDistribution
	Implements ISampleableDistribution(Of Double), IDistribution(Of Double), 
	IDistribution, ICloneable, IRandomNumberGenerator(Of Double), IFittableDistribution(Of Double, GeneralizedBetaOptions), 
	IFittable(Of Double, GeneralizedBetaOptions), IFittable(Of Double), 
	IFittableDistribution(Of Double)

double alpha = 0.42;
double beta = 1.57;

var betaDistribution = new GeneralizedBetaDistribution(alpha, beta);

double mean = betaDistribution.Mean; // 0.21105527638190955
double median = betaDistribution.Median; // 0.11577706212908731
double var = betaDistribution.Variance; // 0.055689279830523512
double mode = betaDistribution.Mode;    // 57.999999999999957

double chf = betaDistribution.CumulativeHazardFunction(x: 0.27); // 1.1828193992944409
double cdf = betaDistribution.DistributionFunction(x: 0.27); // 0.69358638272337991
double pdf = betaDistribution.ProbabilityDensityFunction(x: 0.27); // 0.94644031936694828
double lpdf = betaDistribution.LogProbabilityDensityFunction(x: 0.27); // -0.055047364344046057
double hf = betaDistribution.HazardFunction(x: 0.27); // 3.0887671630877072
double ccdf = betaDistribution.ComplementaryDistributionFunction(x: 0.27); // 0.30641361727662009
double icdf = betaDistribution.InverseDistributionFunction(p: cdf); // 0.26999999068687469

string str = betaDistribution.ToString(System.Globalization.CultureInfo.InvariantCulture); // "B(x; α = 0.42, β = 1.57)

double alpha = 0.42;
double beta = 1.57;

var betaDistribution = new GeneralizedBetaDistribution(alpha, beta);

double mean = betaDistribution.Mean; // 0.21105527638190955
double median = betaDistribution.Median; // 0.11577706212908731
double var = betaDistribution.Variance; // 0.055689279830523512
double mode = betaDistribution.Mode;    // 57.999999999999957

double chf = betaDistribution.CumulativeHazardFunction(x: 0.27); // 1.1828193992944409
double cdf = betaDistribution.DistributionFunction(x: 0.27); // 0.69358638272337991
double pdf = betaDistribution.ProbabilityDensityFunction(x: 0.27); // 0.94644031936694828
double lpdf = betaDistribution.LogProbabilityDensityFunction(x: 0.27); // -0.055047364344046057
double hf = betaDistribution.HazardFunction(x: 0.27); // 3.0887671630877072
double ccdf = betaDistribution.ComplementaryDistributionFunction(x: 0.27); // 0.30641361727662009
double icdf = betaDistribution.InverseDistributionFunction(p: cdf); // 0.26999999068687469

string str = betaDistribution.ToString(System.Globalization.CultureInfo.InvariantCulture); // "B(x; α = 0.42, β = 1.57)

// Create a Beta from a minimum, maximum and most likely value
var b = GeneralizedBetaDistribution.Pert(min: 1, max: 3, mode: 2);

double mean = b.Mean;     // 2
double median = b.Median; // 2
double mode = b.Mode;     // 2
double var = b.Variance;  // 0.071428571428571425

// Create a Beta from a minimum, maximum and most likely value
var b = GeneralizedBetaDistribution.Vose(min: 1, max: 3, mode: 1.42);

double mean = b.Mean;     // 1.6133333333333333
double median = b.Median; // 1.5727889200146494
double mode = b.Mode;     // 1.4471823077804513
double var = b.Variance;  // 0.055555555555555546

// Using the distribution's parameters
double[] samples = GeneralizedBetaDistribution.Random(alpha: 2, beta: 3, min: 0, max: 1, samples: 1000);

// Using an existing distribution
var b = new GeneralizedBetaDistribution(alpha: 1, beta: 2);
double[] new_samples = b.Generate(1000);

// First we will be drawing 100000 observations from a 4-parameter 
//   Beta distribution with α = 2, β = 3, min = 10 and max = 15:

double[] samples = GeneralizedBetaDistribution.Random(alpha: 2, beta: 3, min: 10, max: 15, samples: 100000);

// We can estimate a distribution with the known max and min
var B = GeneralizedBetaDistribution.Estimate(samples, 10, 15);

// We can explicitly ask for a Method-of-moments estimation
var mm = GeneralizedBetaDistribution.Estimate(samples, 10, 15,
    new GeneralizedBetaOptions { Method = BetaEstimationMethod.Moments });

// or explicitly ask for the Maximum Likelihood estimation
var mle = GeneralizedBetaDistribution.Estimate(samples, 10, 15,
    new GeneralizedBetaOptions { Method = BetaEstimationMethod.MaximumLikelihood });