Namespaces

Types in MathNet.Numerics.Distributions

Type BetaScaled

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Constructors

Static Functions

Methods

Properties

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

double CDF(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.

double InvCDF(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.

bool IsValidParameterSet(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.

double PDF(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.

double PDFLn(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.

BetaScaled PERT(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.

double Sample(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.

double Sample(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.

void Samples(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.

void Samples(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

double CumulativeDistribution(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.

double Density(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.

double DensityLn(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.

bool Equals(object obj)

int GetHashCode()

Type GetType()

double InverseCumulativeDistribution(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.

double Sample()

Generates a sample from the distribution.
Return
double

a sample from the distribution.

void Samples(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.

string ToString()

A string representation of the distribution.
Return
string

A string representation of the BetaScaled distribution.

Public Properties

double A get;

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

double B get;

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

double Entropy get;

Gets the entropy of the BetaScaled distribution.

double Location get;

Gets the location (μ) of the BetaScaled distribution.

double Maximum get;

Gets the maximum of the BetaScaled distribution.

double Mean get;

Gets the mean of the BetaScaled distribution.

double Median get;

Gets the median of the BetaScaled distribution.

double Minimum get;

Gets the minimum of the BetaScaled distribution.

double Mode get;

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

Random RandomSource get; set;

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

double Scale get;

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

double Skewness get;

Gets the skewness of the BetaScaled distribution.

double StdDev get;

Gets the standard deviation of the BetaScaled distribution.

double Variance get;

Gets the variance of the BetaScaled distribution.