CauchyDistribution Class

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

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

double location = 0.42;
double scale = 1.57;

// Create a new Cauchy distribution with x0 = 0.42 and γ = 1.57 
CauchyDistribution cauchy = new CauchyDistribution(location, scale);

// Common measures
double mean = cauchy.Mean;     // NaN - Cauchy's mean is undefined.
double var = cauchy.Variance;  // NaN - Cauchy's variance is undefined.
double median = cauchy.Median; // 0.42

// Cumulative distribution functions
double cdf = cauchy.DistributionFunction(x: 0.27);           // 0.46968025841608563
double ccdf = cauchy.ComplementaryDistributionFunction(x: 0.27);          // 0.53031974158391437
double icdf = cauchy.InverseDistributionFunction(p: 0.69358638272337991); // 1.5130304686978195

// Probability density functions
double pdf = cauchy.ProbabilityDensityFunction(x: 0.27);     // 0.2009112009763413
double lpdf = cauchy.LogProbabilityDensityFunction(x: 0.27); // -1.6048922547266871

// Hazard (failure rate) functions
double hf = cauchy.HazardFunction(x: 0.27); // 0.3788491832800277
double chf = cauchy.CumulativeHazardFunction(x: 0.27); // 0.63427516833243092

// String representation
string str = cauchy.ToString(CultureInfo.InvariantCulture); // "Cauchy(x; x0 = 0.42, γ = 1.57)

// Create an initial distribution
CauchyDistribution cauchy = new CauchyDistribution();

// Consider a vector of univariate observations
double[] observations = { 0.25, 0.12, 0.72, 0.21, 0.62, 0.12, 0.62, 0.12 };

// Fit to the observations
cauchy.Fit(observations);

// Check estimated values
double location = cauchy.Location; //  0.18383
double gamma    = cauchy.Scale;    // -0.10530

// Create options to estimate location only
CauchyOptions options = new CauchyOptions()
{
    EstimateLocation = true,
    EstimateScale = false
};

// Create an initial distribution with a pre-defined scale
CauchyDistribution cauchy = new CauchyDistribution(location: 0, scale: 4.2);

// Fit to the observations
cauchy.Fit(observations, options);

// Check estimated values
double location = cauchy.Location; //  0.3471218110202
double gamma    = cauchy.Scale;    //  4.2 (unchanged)