NormalDistribution Class

[SerializableAttribute]
public class NormalDistribution : UnivariateContinuousDistribution, 
	IFittableDistribution<double, NormalOptions>, IFittable<double, NormalOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable, ISampleableDistribution<double>, IRandomNumberGenerator<double>, 
	IFormattable, IUnivariateFittableDistribution, IUnivariateDistribution<double>, IUnivariateDistribution

<SerializableAttribute>
Public Class NormalDistribution
	Inherits UnivariateContinuousDistribution
	Implements IFittableDistribution(Of Double, NormalOptions), 
	IFittable(Of Double, NormalOptions), IFittable(Of Double), 
	IFittableDistribution(Of Double), IDistribution(Of Double), IDistribution, 
	ICloneable, ISampleableDistribution(Of Double), IRandomNumberGenerator(Of Double), 
	IFormattable, IUnivariateFittableDistribution, IUnivariateDistribution(Of Double), IUnivariateDistribution

// Create a normal distribution with mean 2 and sigma 3
var normal = new NormalDistribution(mean: 2, stdDev: 3);

// In a normal distribution, the median and
// the mode coincide with the mean, so

double mean = normal.Mean;     // 2
double mode = normal.Mode;     // 2
double median = normal.Median; // 2

// The variance is the square of the standard deviation
double variance = normal.Variance; // 3² = 9

// Let's check what is the cumulative probability of
// a value less than 3 occurring in this distribution:
double cdf = normal.DistributionFunction(3); // 0.63055

// Finally, let's generate 1000 samples from this distribution
// and check if they have the specified mean and standard devs

double[] samples = normal.Generate(1000);

double sampleMean = samples.Mean();             // 1.92
double sampleDev = samples.StandardDeviation(); // 3.00

var normal = new NormalDistribution(mean: 4, stdDev: 4.2);

double mean = normal.Mean;     // 4.0
double median = normal.Median; // 4.0
double mode = normal.Mode;     // 4.0
double var = normal.Variance;  // 17.64

double cdf = normal.DistributionFunction(x: 1.4);           // 0.26794249453351904
double pdf = normal.ProbabilityDensityFunction(x: 1.4);     // 0.078423391448155175
double lpdf = normal.LogProbabilityDensityFunction(x: 1.4); // -2.5456330358182586

double ccdf = normal.ComplementaryDistributionFunction(x: 1.4); // 0.732057505466481
double icdf = normal.InverseDistributionFunction(p: cdf);       // 1.4

double hf = normal.HazardFunction(x: 1.4);            // 0.10712736480747137
double chf = normal.CumulativeHazardFunction(x: 1.4); // 0.31189620872601354

string str = normal.ToString(CultureInfo.InvariantCulture); // N(x; μ = 4, σ² = 17.64)