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SkewNormalDistribution Class

Skew Normal distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateSkewNormalDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.7.0
Syntax
[SerializableAttribute]
public class SkewNormalDistribution : UnivariateContinuousDistribution
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The SkewNormalDistribution type exposes the following members.

Constructors
  NameDescription
Public methodSkewNormalDistribution
Constructs a Skew normal distribution with zero location, unit scale and zero shape.
Public methodSkewNormalDistribution(Double)
Constructs a Skew normal distribution with given location, unit scale and zero skewness.
Public methodSkewNormalDistribution(Double, Double)
Constructs a Skew normal distribution with given location and scale and zero skewness.
Public methodSkewNormalDistribution(Double, Double, Double)
Constructs a Skew normal distribution with given mean and standard deviation.
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Properties
  NameDescription
Public propertyEntropy
Not supported.
(Overrides UnivariateContinuousDistributionEntropy.)
Public propertyKurtosis
Gets the excess kurtosis for this distribution.
Public propertyLocation
Gets the skew-normal distribution's location value ξ (ksi).
Public propertyMean
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)
Public propertyMedian
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyMode
Gets the mode for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyScale
Gets the skew-normal distribution's scale value ω (omega).
Public propertyShape
Gets the skew-normal distribution's shape value α (alpha).
Public propertySkewness
Gets the skewness for this distribution.
Public propertyStandardDeviation
Gets the Standard Deviation (the square root of the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertySupport
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)
Public propertyVariance
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.)
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)
Public methodComplementaryDistributionFunction
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.)
Public methodCumulativeHazardFunction
Gets the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double)
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(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.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Int32, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Random)
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRange
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazardFunction
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.)
Protected methodInnerComplementaryDistributionFunction
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.)
Protected methodInnerDistributionFunction
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
Protected methodInnerInverseDistributionFunction
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.)
Protected methodInnerLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
Protected methodInnerProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
Public methodInverseDistributionFunction
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.)
Public methodLogCumulativeHazardFunction
Gets the log of the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodStatic memberNormal
Create a new SkewNormalDistribution that corresponds to a NormalDistribution with the given mean and standard deviation.
Public methodProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodQuantileDensityFunction
Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
(Inherited from UnivariateContinuousDistribution.)
Public methodToString
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(IFormatProvider)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String, IFormatProvider)
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
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

In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.

References:

Examples

This examples shows how to create a Skew normal distribution and compute some of its properties and derived measures.

// Create a Skew normal distribution with location 2, scale 3 and shape 4.2
var skewNormal = new SkewNormalDistribution(location: 2, scale: 3, shape: 4.2);

double mean = skewNormal.Mean;     // 4.3285611780515953
double median = skewNormal.Median; // 4.0230040653062265
double var = skewNormal.Variance;  // 3.5778028400709641
double mode = skewNormal.Mode;     // 3.220622226764422

double cdf = skewNormal.DistributionFunction(x: 1.4); // 0.020166854942526125
double pdf = skewNormal.ProbabilityDensityFunction(x: 1.4); // 0.052257431834162059
double lpdf = skewNormal.LogProbabilityDensityFunction(x: 1.4); // -2.9515731621912877

double ccdf = skewNormal.ComplementaryDistributionFunction(x: 1.4); // 0.97983314505747388
double icdf = skewNormal.InverseDistributionFunction(p: cdf); // 1.3999998597203041

double hf = skewNormal.HazardFunction(x: 1.4); // 0.053332990517581239
double chf = skewNormal.CumulativeHazardFunction(x: 1.4); // 0.020372981958858238

string str = skewNormal.ToString(CultureInfo.InvariantCulture); // Sn(x; ξ = 2, ω = 3, α = 4.2)
See Also