ShapiroWilkDistribution Class

Shapiro-Wilk distribution.

Inheritance Hierarchy

SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateShapiroWilkDistribution

Namespace: Accord.Statistics.Distributions.Univariate
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0

Syntax

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[SerializableAttribute]
public class ShapiroWilkDistribution : UnivariateContinuousDistribution, 
	IFormattable

<SerializableAttribute>
Public Class ShapiroWilkDistribution
	Inherits UnivariateContinuousDistribution
	Implements IFormattable

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The ShapiroWilkDistribution type exposes the following members.

Constructors

	Name	Description
	ShapiroWilkDistribution	Creates a new Shapiro-Wilk distribution.

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Properties

	Name	Description
	Entropy	Not supported. (Overrides UnivariateContinuousDistributionEntropy.)
	Mean	Gets the mean for this distribution. (Overrides UnivariateContinuousDistributionMean.)
	Median	Gets the median for this distribution. (Overrides UnivariateContinuousDistributionMedian.)
	Mode	Gets the mode for this distribution. (Overrides UnivariateContinuousDistributionMode.)
	NumberOfSamples	Gets the number of samples distribution parameter.
	Quartiles	Gets the Quartiles for this distribution. (Inherited from UnivariateContinuousDistribution.)
	StandardDeviation	Gets the Standard Deviation (the square root of the variance) for the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Support	Gets the support interval for this distribution. (Overrides UnivariateContinuousDistributionSupport.)
	Variance	Not supported. (Overrides UnivariateContinuousDistributionVariance.)

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Methods

	Name	Description
	Clone	Creates a new object that is a copy of the current instance. (Overrides DistributionBaseClone.)
	ComplementaryDistributionFunction	Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function. (Inherited from UnivariateContinuousDistribution.)
	CumulativeHazardFunction	Gets the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(Double)	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(Double, Double)	Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b). (Inherited from UnivariateContinuousDistribution.)
	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.)
	Fit(Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double, IFittingOptions)	Not supported. (Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
	Fit(Double, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Generate	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Random)	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRange	Gets the distribution range within a given percentile. (Inherited from UnivariateContinuousDistribution.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	HazardFunction	Gets the hazard function, also known as the failure rate or the conditional failure density function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	InnerComplementaryDistributionFunction	Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function. (Overrides UnivariateContinuousDistributionInnerComplementaryDistributionFunction(Double).)
	InnerDistributionFunction	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
	InnerInverseDistributionFunction	Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function. (Inherited from UnivariateContinuousDistribution.)
	InnerLogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
	InnerProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
	InverseDistributionFunction	Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function. (Inherited from UnivariateContinuousDistribution.)
	LogCumulativeHazardFunction	Gets the log of the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	LogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	QuantileDensityFunction	Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p. (Inherited from UnivariateContinuousDistribution.)
	ToString	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(IFormatProvider)	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(String)	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(String, IFormatProvider)	Returns a String that represents this instance. (Overrides DistributionBaseToString(String, IFormatProvider).)

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Extension Methods

	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)
	ToT	Overloaded. Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime. (Defined by ExtensionMethods.)

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Remarks

The Shapiro-Wilk distribution models the distribution of Shapiro-Wilk's test statistic.

References:

Royston, P. "Algorithm AS 181: The W test for Normality", Applied Statistics (1982), Vol. 31, pp. 176–180.
Royston, P. "Remark AS R94", Applied Statistics (1995), Vol. 44, No. 4, pp. 547-551. Available at http://lib.stat.cmu.edu/apstat/R94
Royston, P. "Approximating the Shapiro-Wilk W-test for non-normality", Statistics and Computing (1992), Vol. 2, pp. 117-119.
Royston, P. "An Extension of Shapiro and Wilk's W Test for Normality to Large Samples", Journal of the Royal Statistical Society Series C (1982a), Vol. 31, No. 2, pp. 115-124.

Examples

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// Create a new Shapiro-Wilk's W for 5 samples
var sw = new ShapiroWilkDistribution(samples: 5);

double mean = sw.Mean;     // 0.81248567196628929
double median = sw.Median; // 0.81248567196628929
double mode = sw.Mode;     // 0.81248567196628929

double cdf = sw.DistributionFunction(x: 0.84); // 0.83507812080728383
double pdf = sw.ProbabilityDensityFunction(x: 0.84); // 0.82021062372326459
double lpdf = sw.LogProbabilityDensityFunction(x: 0.84); // -0.1981941135071546

double ccdf = sw.ComplementaryDistributionFunction(x: 0.84); // 0.16492187919271617
double icdf = sw.InverseDistributionFunction(p: cdf); // 0.84000000194587177

double hf = sw.HazardFunction(x: 0.84); // 4.9733281462602292
double chf = sw.CumulativeHazardFunction(x: 0.84); // 1.8022833766369502

string str = sw.ToString(CultureInfo.InvariantCulture); // W(x; n = 12)

Reference

Accord.Statistics.Distributions.Univariate Namespace