CauchyDistribution Class
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CauchyDistribution Class

Represents a Cauchy distribution.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 4.0.5.0 (4.0.5.0)
Syntax
public sealed class CauchyDistribution : ContinuousDistribution

The CauchyDistribution type exposes the following members.

Constructors
  NameDescription
Public methodCauchyDistribution
Initializes a new standard Cauchy distribution.
Public methodCauchyDistribution(Double, Double)
Initializes a new Cauchy distribution.
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Properties
  NameDescription
Public propertyExcessKurtosis
Gets the excess kurtosis of the distribution.
(Inherited from UnivariateDistribution.)
Public propertyFullWithAtHalfMaximum
Gets the full width at half maximum (FWHM) of the Cauchy distribution.
Public propertyMean
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)
Public propertyMedian
Gets the median of the distribution.
(Overrides ContinuousDistributionMedian.)
Public propertySkewness
Gets the skewness of the distribution.
(Inherited from UnivariateDistribution.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)
Public propertySupport
Gets the interval over which the distribution is non-vanishing.
(Inherited from ContinuousDistribution.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.)
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Methods
  NameDescription
Public methodCentralMoment
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)
Public methodCumulant
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodExpectationValue
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRandomValue
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)
Public methodGetRandomValues
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazard
Computes the hazard function.
(Inherited from ContinuousDistribution.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Overrides ContinuousDistributionInverseRightProbability(Double).)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)
Public methodRawMoment
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)
Public methodRightProbability
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

In physical applications, the Cauchy distribution is usually called a Lorentz distribution. It models the shape of a spectral line.

The Cauchy distribution has "fat tails". In fact, it falls off at the minimum possible rate consistent with having a convergent integral. For this same reason, none of its moments (above the zeroth) are defined.

See Also