WrappedCauchyDistribution Class

Wrapped Cauchy Distribution.

Inheritance Hierarchy

SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateWrappedCauchyDistribution

Namespace: Accord.Statistics.Distributions.Univariate
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0

Syntax

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public class WrappedCauchyDistribution : UnivariateContinuousDistribution, 
	IFittableDistribution<double, CauchyOptions>, IFittable<double, CauchyOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable

Public Class WrappedCauchyDistribution
	Inherits UnivariateContinuousDistribution
	Implements IFittableDistribution(Of Double, CauchyOptions), 
	IFittable(Of Double, CauchyOptions), IFittable(Of Double), 
	IFittableDistribution(Of Double), IDistribution(Of Double), IDistribution, 
	ICloneable

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The WrappedCauchyDistribution type exposes the following members.

Constructors

	Name	Description
	WrappedCauchyDistribution	Initializes a new instance of the WrappedCauchyDistribution class.

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Properties

	Name	Description
	Entropy	Gets the entropy for this distribution. (Overrides UnivariateContinuousDistributionEntropy.)
	Mean	Gets the mean for this distribution. (Overrides UnivariateContinuousDistributionMean.)
	Median	Not supported. (Overrides UnivariateContinuousDistributionMedian.)
	Mode	Not supported. (Overrides UnivariateContinuousDistributionMode.)
	Quartiles	Gets the Quartiles for this distribution. (Inherited from UnivariateContinuousDistribution.)
	StandardDeviation	Gets the Standard Deviation (the square root of the variance) for the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Support	Gets the support interval for this distribution. (Overrides UnivariateContinuousDistributionSupport.)
	Variance	Gets the variance for this distribution. (Overrides UnivariateContinuousDistributionVariance.)

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Methods

	Name	Description
	Clone	Creates a new object that is a copy of the current instance. (Overrides DistributionBaseClone.)
	ComplementaryDistributionFunction	Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function. (Inherited from UnivariateContinuousDistribution.)
	CumulativeHazardFunction	Gets the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(Double)	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(Double, Double)	Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b). (Inherited from UnivariateContinuousDistribution.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	Fit(Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double, CauchyOptions)	Fits the underlying distribution to a given set of observations.
	Fit(Double, Int32, CauchyOptions)	Fits the underlying distribution to a given set of observations.
	Generate	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Random)	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRange	Gets the distribution range within a given percentile. (Inherited from UnivariateContinuousDistribution.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	HazardFunction	Gets the hazard function, also known as the failure rate or the conditional failure density function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	InnerComplementaryDistributionFunction	Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function. (Inherited from UnivariateContinuousDistribution.)
	InnerDistributionFunction	Not supported. (Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
	InnerInverseDistributionFunction	Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function. (Inherited from UnivariateContinuousDistribution.)
	InnerLogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
	InnerProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
	InverseDistributionFunction	Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function. (Inherited from UnivariateContinuousDistribution.)
	LogCumulativeHazardFunction	Gets the log of the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	LogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	QuantileDensityFunction	Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p. (Inherited from UnivariateContinuousDistribution.)
	ToString	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(IFormatProvider)	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(String)	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(String, IFormatProvider)	Returns a String that represents this instance. (Overrides DistributionBaseToString(String, IFormatProvider).)

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Extension Methods

	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)
	ToT	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)

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Remarks

In probability theory and directional statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit circle. The Cauchy distribution is sometimes known as a Lorentzian distribution, and the wrapped Cauchy distribution may sometimes be referred to as a wrapped Lorentzian distribution.

The wrapped Cauchy distribution is often found in the field of spectroscopy where it is used to analyze diffraction patterns (e.g. see Fabry–Pérot interferometer)

References:

Examples

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// Create a Wrapped Cauchy distribution with μ = 0.42, γ = 3
var dist = new WrappedCauchyDistribution(mu: 0.42, gamma: 3);

// Common measures
double mean = dist.Mean;     // 0.42
double var = dist.Variance;  // 0.950212931632136

// Probability density functions
double pdf = dist.ProbabilityDensityFunction(x: 0.42); // 0.1758330112785475
double lpdf = dist.LogProbabilityDensityFunction(x: 0.42); // -1.7382205338929015

// String representation
string str = dist.ToString(); // "WrappedCauchy(x; μ = 0,42, γ = 3)"

Reference

Accord.Statistics.Distributions.Univariate Namespace

Accord.Statistics.Distributions.UnivariateCauchyDistribution