BetaDistribution Class

[SerializableAttribute]
public class BetaDistribution : UnivariateContinuousDistribution, 
	IFormattable, IFittableDistribution<double, BetaOptions>, IFittable<double, BetaOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable, ISampleableDistribution<double>, IRandomNumberGenerator<double>

<SerializableAttribute>
Public Class BetaDistribution
	Inherits UnivariateContinuousDistribution
	Implements IFormattable, IFittableDistribution(Of Double, BetaOptions), 
	IFittable(Of Double, BetaOptions), IFittable(Of Double), 
	IFittableDistribution(Of Double), IDistribution(Of Double), IDistribution, 
	ICloneable, ISampleableDistribution(Of Double), IRandomNumberGenerator(Of Double)

double alpha = 0.42;
double beta = 1.57;

// Create a new Beta distribution with α = 0.42 and β = 1.57
BetaDistribution distribution = new BetaDistribution(alpha, beta);

// Common measures
double mean   = distribution.Mean;      // 0.21105527638190955
double median = distribution.Median;    // 0.11577711097114812
double var    = distribution.Variance;  // 0.055689279830523512

// Cumulative distribution functions
double cdf    = distribution.DistributionFunction(x: 0.27);          // 0.69358638272337991
double ccdf   = distribution.ComplementaryDistributionFunction(x: 0.27); // 0.30641361727662009
double icdf   = distribution.InverseDistributionFunction(p: cdf);        // 0.26999999068687469

// Probability density functions
double pdf    = distribution.ProbabilityDensityFunction(x: 0.27);    // 0.94644031936694828
double lpdf   = distribution.LogProbabilityDensityFunction(x: 0.27); // -0.055047364344046057

// Hazard (failure rate) functions
double hf     = distribution.HazardFunction(x: 0.27);           // 3.0887671630877072
double chf    = distribution.CumulativeHazardFunction(x: 0.27); // 1.1828193992944409

// String representation
string str = distribution.ToString(); // B(x; α = 0.42, β = 1.57)

int trials = 100;
int successes = 78;

BetaDistribution distribution = new BetaDistribution(successes, trials);

double mean   = distribution.Mean; // 0.77450980392156865
double median = distribution.Median; // 0.77630912598534851

double p025   = distribution.InverseDistributionFunction(p: 0.025); // 0.68899653915764347
double p975   = distribution.InverseDistributionFunction(p: 0.975); // 0.84983461640764513

// 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);

// Draw 100000 observations from a Beta with α = 2, β = 3:
double[] samples = GeneralizedBetaDistribution
    .Random(alpha: 2, beta: 3, samples: 100000);

// Estimate a distribution from the data
var B = BetaDistribution.Estimate(samples);

// Explicitly using Method-of-moments estimation
var mm = BetaDistribution.Estimate(samples,
    new BetaOptions { Method = BetaEstimationMethod.Moments });

// Explicitly using Maximum Likelihood estimation
var mle = BetaDistribution.Estimate(samples,
    new BetaOptions { Method = BetaEstimationMethod.MaximumLikelihood });