Types in MathNet.Numerics.Distributions

Type Cauchy

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Continuous Univariate Cauchy distribution. The Cauchy distribution is a symmetric continuous probability distribution. For details about this distribution, see.

Public Constructors

Cauchy(double location, double scale, Random randomSource)

Initializes a new instance of the Cauchy class.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

`Random` randomSource

The random number generator which is used to draw random samples.

Cauchy()

Initializes a new instance of the Cauchy class with the location parameter set to 0 and the scale parameter set to 1

Cauchy(double location, double scale)

Initializes a new instance of the Cauchy class.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Public Static Functions

doubleCDF(double location, double scale, double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

`double` x

The location at which to compute the cumulative distribution function.

Return
`double`

the cumulative distribution at location x.

doubleInvCDF(double location, double scale, double p)

Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

`double` p

The location at which to compute the inverse cumulative density.

Return
`double`

the inverse cumulative density at p.

boolIsValidParameterSet(double location, double scale)

Tests whether the provided values are valid parameters for this distribution.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

doublePDF(double location, double scale, double x)

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

`double` x

The location at which to compute the density.

Return
`double`

the density at x.

doublePDFLn(double location, double scale, double x)

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

`double` x

The location at which to compute the density.

Return
`double`

the log density at x.

doubleSample(Random rnd, double location, double scale)

Generates a sample from the distribution.
Parameters
`Random` rnd

The random number generator to use.

`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Return
`double`

a sample from the distribution.

doubleSample(double location, double scale)

Generates a sample from the distribution.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Return
`double`

a sample from the distribution.

IEnumerable<double>Samples(Random rnd, double location, double scale)

Generates a sequence of samples from the distribution.
Parameters
`Random` rnd

The random number generator to use.

`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Return
`IEnumerable<double>`

a sequence of samples from the distribution.

voidSamples(Random rnd, Double[] values, double location, double scale)

Fills an array with samples generated from the distribution.
Parameters
`Random` rnd

The random number generator to use.

`Double[]` values

The array to fill with the samples.

`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Return
`void`

a sequence of samples from the distribution.

IEnumerable<double>Samples(double location, double scale)

Generates a sequence of samples from the distribution.
Parameters
`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Return
`IEnumerable<double>`

a sequence of samples from the distribution.

voidSamples(Double[] values, double location, double scale)

Fills an array with samples generated from the distribution.
Parameters
`Double[]` values

The array to fill with the samples.

`double` location

The location (x0) of the distribution.

`double` scale

The scale (γ) of the distribution. Range: γ > 0.

Return
`void`

a sequence of samples from the distribution.

Public Methods

doubleCumulativeDistribution(double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Parameters
`double` x

The location at which to compute the cumulative distribution function.

Return
`double`

the cumulative distribution at location x.

doubleDensity(double x)

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
Parameters
`double` x

The location at which to compute the density.

Return
`double`

the density at x.

doubleDensityLn(double x)

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
Parameters
`double` x

The location at which to compute the log density.

Return
`double`

the log density at x.

doubleInverseCumulativeDistribution(double p)

Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.
Parameters
`double` p

The location at which to compute the inverse cumulative density.

Return
`double`

the inverse cumulative density at p.

doubleSample()

Draws a random sample from the distribution.
Return
`double`

A random number from this distribution.

IEnumerable<double>Samples()

Generates a sequence of samples from the Cauchy distribution.
Return
`IEnumerable<double>`

a sequence of samples from the distribution.

voidSamples(Double[] values)

Fills an array with samples generated from the distribution.

stringToString()

A string representation of the distribution.
Return
`string`

a string representation of the distribution.

Public Properties

doubleEntropy get;

Gets the entropy of the distribution.

doubleLocation get;

Gets the location (x0) of the distribution.

doubleMaximum get;

Gets the maximum of the distribution.

doubleMean get;

Gets the mean of the distribution.

doubleMedian get;

Gets the median of the distribution.

doubleMinimum get;

Gets the minimum of the distribution.

doubleMode get;

Gets the mode of the distribution.

RandomRandomSource get; set;

Gets or sets the random number generator which is used to draw random samples.

doubleScale get;

Gets the scale (γ) of the distribution. Range: γ > 0.

doubleSkewness get;

Gets the skewness of the distribution.

doubleStdDev get;

Gets the standard deviation of the distribution.

doubleVariance get;

Gets the variance of the distribution.