SkewedGeneralizedT Class

Continuous Univariate Skewed Generalized T-distribution. Implements the univariate Skewed Generalized t-distribution. For details about this distribution, see Wikipedia - Skewed generalized t-distribution. The skewed generalized t-distribution contains many different distributions within it as special cases based on the parameterization chosen.

Inheritance Hierarchy

SystemObject
Altaxo.Calc.DistributionsSkewedGeneralizedT

Namespace: Altaxo.Calc.Distributions
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)

Syntax

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public class SkewedGeneralizedT : IContinuousDistribution, 
	IUnivariateDistribution, IDistribution

The SkewedGeneralizedT type exposes the following members.

Constructors

	Name	Description
	SkewedGeneralizedT	Initializes a new instance of the SkewedGeneralizedT class. This is a skewed generalized t-distribution with location=0.0, scale=1.0, skew=0.0, p=2.0 and q=Inf (a standard normal distribution).
	SkewedGeneralizedT(Double, Double, Double, Double, Double)	Initializes a new instance of the SkewedGeneralizedT class with a particular location, scale, skew and kurtosis parameters. Different parameterizations result in different distributions.

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Properties

	Name	Description
	Entropy	Gets the entropy of the distribution.
	Location	Gets the location (μ) of the Skewed Generalized t-distribution.
	Maximum	Gets the largest element in the domain of the distribution which can be represented by a double.
	Mean	Gets the mean of the distribution.
	Median	Gets the median of the distribution.
	Minimum	Gets the smallest element in the domain of the distribution which can be represented by a double.
	Mode	Gets the mode of the distribution.
	P	Gets the first parameter that controls the kurtosis of the distribution. Range: p > 0.
	Q	Gets the second parameter that controls the kurtosis of the distribution. Range: q > 0.
	RandomSource	Gets or sets the random number generator which is used to draw random samples.
	Scale	Gets the scale (σ) of the Skewed Generalized t-distribution. Range: σ > 0.
	Skew	Gets the skew (λ) of the Skewed Generalized t-distribution. Range: 1 > λ > -1.
	Skewness	Gets the skewness of the distribution.
	StdDev	Gets the standard deviation of the distribution.
	Variance	Gets the variance of the distribution.

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Methods

	Name	Description
	CDF	Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
	CumulativeDistribution	Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
	Density	Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
	DensityLn	Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
	FindSpecializedDistribution	Given a parameter set, returns the distribution that matches this parameterization.
	GetHashCode	Serves as the default hash function. (Inherited from Object)
	GetType	Gets the Type of the current instance. (Inherited from Object)
	InvCDF	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.
	InverseCumulativeDistribution	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.
	IsValidParameterSet	Tests whether the provided values are valid parameters for this distribution.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	PDF	Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
	PDFLn	Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
	Sample	Draws a random sample from the distribution.
	Sample(Double, Double, Double, Double, Double)	Generates a sample from the Skew Generalized t-distribution.
	Sample(Random, Double, Double, Double, Double, Double)	Generates a sample from the Skew Generalized t-distribution.
	Samples	Draws a sequence of random samples from the distribution.
	Samples(Double)	Fills an array with samples generated from the distribution.
	Samples(Double, Double, Double, Double, Double)	Generates a sequence of samples from the Skew Generalized t-distribution using inverse transform.
	Samples(Double, Double, Double, Double, Double, Double)	Fills an array with samples from the Skew Generalized t-distribution using inverse transform.
	Samples(Random, Double, Double, Double, Double, Double)	Generates a sequence of samples from the Skew Generalized t-distribution using inverse transform.
	Samples(Random, Double, Double, Double, Double, Double, Double)	Fills an array with samples from the Skew Generalized t-distribution using inverse transform.
	ToString	A string representation of the distribution. (Overrides ObjectToString)

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Remarks

This implementation is based on the R package dsgt and corresponding vignette, see https://cran.r-project.org/web/packages/sgt/vignettes/sgt.pdf. Compared to that implementation, the options for mean adjustment and variance adjustment are always true. The location (μ) is the mean of the distribution. The scale (σ) squared is the variance of the distribution.

The distribution will use the Random by default. Users can get/set the random number generator by using the RandomSource property.

The statistics classes will check all the incoming parameters whether they are in the allowed range.

Reference

Altaxo.Calc.Distributions Namespace