## Types in MathNet.Numerics.Distributions

Type BetaScaled

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

### Public Constructors

#### BetaScaled(double a, double b, double location, double scale, Random randomSource)

Initializes a new instance of the BetaScaled class.
##### Parameters
###### `double` a

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

###### `Random` randomSource

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

#### BetaScaled(double a, double b, double location, double scale)

Initializes a new instance of the BetaScaled class.
##### Parameters
###### `double` a

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

### Public Static Functions

#### doubleCDF(double a, double b, double location, double scale, 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 BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

The scale (σ) of the distribution. Range: σ > 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 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.
WARNING: currently not an explicit implementation, hence slow and unreliable.
##### Parameters
###### `double` a

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

The scale (σ) of the distribution. Range: σ > 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, double location, double scale)

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

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

#### doublePDF(double a, double b, double location, double scale, 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 BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

###### `double` x

The location at which to compute the density.

##### Return
###### `double`

the density at x.

#### doublePDFLn(double a, double b, 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` a

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

###### `double` x

The location at which to compute the density.

##### Return
###### `double`

the log density at x.

#### BetaScaledPERT(double min, double max, double likely, Random randomSource)

Create a Beta PERT distribution, used in risk analysis and other domains where an expert forecast is used to construct an underlying beta distribution.
##### Parameters
###### `double` min

The minimum value.

###### `double` max

The maximum value.

###### `double` likely

The most likely value (mode).

###### `Random` randomSource

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

##### Return
###### `BetaScaled`

The Beta distribution derived from the PERT parameters.

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

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

The random number generator to use.

###### `double` a

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

##### Return
###### `double`

a sample from the distribution.

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

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

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

##### Return
###### `double`

a sample from the distribution.

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

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 BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

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

a sequence of samples from the distribution.

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

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

##### Return
###### `void`

a sequence of samples from the distribution.

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

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

The α shape parameter of the BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

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

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

a sequence of samples from the distribution.

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

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 BetaScaled distribution. Range: α > 0.

###### `double` b

The β shape parameter of the BetaScaled distribution. Range: β > 0.

###### `double` location

The location (μ) of the distribution.

###### `double` scale

The scale (σ) of the distribution. Range: σ > 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 distribution.
##### Return
###### `double`

a sample from the distribution.

#### voidSamples(Double[] values)

Fills an array with samples generated from the distribution.

#### IEnumerable<double>Samples()

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

a sequence of samples from the distribution.

#### stringToString()

A string representation of the distribution.
##### Return
###### `string`

A string representation of the BetaScaled distribution.

### Public Properties

#### doubleA get;

Gets the α shape parameter of the BetaScaled distribution. Range: α > 0.

#### doubleB get;

Gets the β shape parameter of the BetaScaled distribution. Range: β > 0.

#### doubleEntropy get;

Gets the entropy of the BetaScaled distribution.

#### doubleLocation get;

Gets the location (μ) of the BetaScaled distribution.

#### doubleMaximum get;

Gets the maximum of the BetaScaled distribution.

#### doubleMean get;

Gets the mean of the BetaScaled distribution.

#### doubleMedian get;

Gets the median of the BetaScaled distribution.

#### doubleMinimum get;

Gets the minimum of the BetaScaled distribution.

#### doubleMode get;

Gets the mode of the BetaScaled 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.

#### doubleScale get;

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

#### doubleSkewness get;

Gets the skewness of the BetaScaled distribution.

#### doubleStdDev get;

Gets the standard deviation of the BetaScaled distribution.

#### doubleVariance get;

Gets the variance of the BetaScaled distribution.