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PowerNormalDistribution Class

Power Normal distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariatePowerNormalDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax
[SerializableAttribute]
public class PowerNormalDistribution : UnivariateContinuousDistribution
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The PowerNormalDistribution type exposes the following members.

Constructors
  NameDescription
Public methodPowerNormalDistribution
Constructs a Power Normal distribution with given power (shape) parameter.
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Properties
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 methodCode exampleFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(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.
(Overrides UnivariateContinuousDistributionInnerInverseDistributionFunction(Double).)
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 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 MethodTo(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.)
Public Extension MethodToTOverloaded.
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
Examples

This example shows how to create a Power Normal distribution and compute some of its properties.

// Create a new Power-Normal distribution with p = 4.2
var pnormal = new PowerNormalDistribution(power: 4.2);

double cdf = pnormal.DistributionFunction(x: 1.4); // 0.99997428721920678
double pdf = pnormal.ProbabilityDensityFunction(x: 1.4); // 0.00020022645890003279
double lpdf = pnormal.LogProbabilityDensityFunction(x: 1.4); // -0.20543269836728234

double ccdf = pnormal.ComplementaryDistributionFunction(x: 1.4); // 0.000025712780793218926
double icdf = pnormal.InverseDistributionFunction(p: cdf); // 1.3999999999998953

double hf = pnormal.HazardFunction(x: 1.4); // 7.7870402470368854
double chf = pnormal.CumulativeHazardFunction(x: 1.4); // 10.568522382550167

string str = pnormal.ToString(); // PND(x; p = 4.2)
See Also