## Types in MathNet.Numerics.Distributions

Type Beta

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

There are a few special cases for the parameterization of the Beta distribution. When both shape parameters are positive infinity, the Beta distribution degenerates to a point distribution at 0.5. When one of the shape parameters is positive infinity, the distribution degenerates to a point distribution at the positive infinity. When both shape parameters are 0.0, the Beta distribution degenerates to a Bernoulli distribution with parameter 0.5. When one shape parameter is 0.0, the distribution degenerates to a point distribution at the non-zero shape parameter.

### Public Constructors

#### Beta(double a, double b, Random randomSource)

Initializes a new instance of the Beta class.
##### Parameters
###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

###### Random randomSource

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

#### Beta(double a, double b)

Initializes a new instance of the Beta class.
##### Parameters
###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

### Public Static Functions

#### doubleCDF(double a, double b, double x)

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

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

###### double x

The location at which to compute the cumulative distribution function.

##### Return
###### double

the cumulative distribution at location x.

#### doubleInvCDF(double a, double b, 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.
WARNING: currently not an explicit implementation, hence slow and unreliable.
##### Parameters
###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

###### double p

The location at which to compute the inverse cumulative density.

##### Return
###### double

the inverse cumulative density at p.

#### boolIsValidParameterSet(double a, double b)

Tests whether the provided values are valid parameters for this distribution.
##### Parameters
###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

#### doublePDF(double a, double b, double x)

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

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

###### double x

The location at which to compute the density.

##### Return
###### double

the density at x.

#### doublePDFLn(double a, double b, double x)

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

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

###### double x

The location at which to compute the density.

##### Return
###### double

the log density at x.

#### doubleSample(double a, double b)

Generates a sample from the distribution.
##### Parameters
###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

##### Return
###### double

a sample from the distribution.

#### doubleSample(Random rnd, double a, double b)

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

The random number generator to use.

###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

##### Return
###### double

a sample from the distribution.

#### IEnumerable<double>Samples(Random rnd, double a, double b)

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

The random number generator to use.

###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

##### Return
###### IEnumerable<double>

a sequence of samples from the distribution.

#### IEnumerable<double>Samples(double a, double b)

Generates a sequence of samples from the distribution.
##### Parameters
###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

##### Return
###### IEnumerable<double>

a sequence of samples from the distribution.

#### voidSamples(Double[] values, double a, double b)

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

The array to fill with the samples.

###### double a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 0.

##### Return
###### void

a sequence of samples from the distribution.

#### voidSamples(Random rnd, Double[] values, double a, double b)

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 a

The α shape parameter of the Beta distribution. Range: α ≥ 0.

###### double b

The β shape parameter of the Beta distribution. Range: β ≥ 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.
WARNING: currently not an explicit implementation, hence slow and unreliable.
##### Parameters
###### double p

The location at which to compute the inverse cumulative density.

##### Return
###### double

the inverse cumulative density at p.

#### doubleSample()

Generates a sample from the Beta distribution.
##### Return
###### double

a sample from the distribution.

#### IEnumerable<double>Samples()

Generates a sequence of samples from the Beta 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 Beta distribution.

### Public Properties

#### doubleA get;

Gets the α shape parameter of the Beta distribution. Range: α ≥ 0.

#### doubleB get;

Gets the β shape parameter of the Beta distribution. Range: β ≥ 0.

#### doubleEntropy get;

Gets the entropy of the Beta distribution.

#### doubleMaximum get;

Gets the maximum of the Beta distribution.

#### doubleMean get;

Gets the mean of the Beta distribution.

#### doubleMedian get;

Gets the median of the Beta distribution.

#### doubleMinimum get;

Gets the minimum of the Beta distribution.

#### doubleMode get;

Gets the mode of the Beta distribution; when there are multiple answers, this routine will return 0.5.

#### RandomRandomSource get; set;

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

#### doubleSkewness get;

Gets the skewness of the Beta distribution.

#### doubleStdDev get;

Gets the standard deviation of the Beta distribution.

#### doubleVariance get;

Gets the variance of the Beta distribution.