CauchyDistribution Class |
Represents a Cauchy distribution.
Inheritance HierarchySystemObject
Meta.Numerics.Statistics.DistributionsUnivariateDistribution
Meta.Numerics.Statistics.DistributionsContinuousDistribution
Meta.Numerics.Statistics.DistributionsCauchyDistribution
Meta.Numerics.Statistics.DistributionsUnivariateDistribution
Meta.Numerics.Statistics.DistributionsContinuousDistribution
Meta.Numerics.Statistics.DistributionsCauchyDistribution
Namespace: Meta.Numerics.Statistics.Distributions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 4.1.4
SyntaxThe CauchyDistribution type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | CauchyDistribution |
Initializes a new standard Cauchy distribution.
|
| CauchyDistribution(Double, Double) |
Initializes a new Cauchy distribution.
|
Properties| Name | Description | |
|---|---|---|
 | ExcessKurtosis |
Gets the excess kurtosis of the distribution.
(Inherited from UnivariateDistribution.) |
| FullWithAtHalfMaximum |
Gets the full width at half maximum (FWHM) of the Cauchy distribution.
|
| Mean |
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.) |
| Median |
Gets the median of the distribution.
(Overrides ContinuousDistributionMedian.) |
| Skewness |
Gets the skewness of the distribution.
(Inherited from UnivariateDistribution.) |
| StandardDeviation |
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.) |
| Support |
Gets the interval over which the distribution is non-vanishing.
(Inherited from ContinuousDistribution.) |
| Variance |
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.) |
Methods| Name | Description | |
|---|---|---|
| CentralMoment |
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).) |
| Cumulant |
Computes a cumulant of the distribution.
(Overrides UnivariateDistributionCumulant(Int32).) |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
| ExpectationValue |
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.) |
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetRandomValue |
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).) |
| GetRandomValues |
Generates the given number of random variates.
(Inherited from ContinuousDistribution.) |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| Hazard |
Computes the hazard function.
(Inherited from ContinuousDistribution.) |
| InverseLeftProbability |
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).) |
| InverseRightProbability |
Returns the point at which the right probability function attains the given value.
(Overrides ContinuousDistributionInverseRightProbability(Double).) |
| LeftProbability |
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).) |
| ProbabilityDensity |
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).) |
| RawMoment |
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).) |
| RightProbability |
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).) |
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
RemarksIn physical applications, the Cauchy distribution is usually called a Lorentz distribution. It models the shape of a spectral line.
The ratio of two normally distributed quantities has a Cauchy distribution.
The Cauchy distribution has "fat tails". In fact, it falls off at the minimum possible rate consistent with having a convergent probability integral. For this same reason, none of its moments (above the zeroth) are defined.
See Also