UnivariateDiscreteDistribution Class

Abstract class for univariate discrete probability distributions.

Inheritance Hierarchy

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

Syntax

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[SerializableAttribute]
public abstract class UnivariateDiscreteDistribution : DistributionBase, 
	IUnivariateDistribution<int>, IDistribution<int>, IDistribution, ICloneable, 
	IUnivariateDistribution, IUnivariateDistribution<double>, IDistribution<double>, 
	IDistribution<double[]>, ISampleableDistribution<double>, IRandomNumberGenerator<double>, 
	ISampleableDistribution<int>, IRandomNumberGenerator<int>, IFormattable

<SerializableAttribute>
Public MustInherit Class UnivariateDiscreteDistribution
	Inherits DistributionBase
	Implements IUnivariateDistribution(Of Integer), IDistribution(Of Integer), 
	IDistribution, ICloneable, IUnivariateDistribution, IUnivariateDistribution(Of Double), 
	IDistribution(Of Double), IDistribution(Of Double()), 
	ISampleableDistribution(Of Double), IRandomNumberGenerator(Of Double), ISampleableDistribution(Of Integer), 
	IRandomNumberGenerator(Of Integer), IFormattable

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The UnivariateDiscreteDistribution type exposes the following members.

Constructors

	Name	Description
	UnivariateDiscreteDistribution	Constructs a new UnivariateDistribution class.

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Properties

	Name	Description
	Entropy	Gets the entropy for this distribution.
	Mean	Gets the mean for this distribution.
	Median	Gets the median for this distribution.
	Mode	Gets the mode for this distribution.
	Quartiles	Gets the Quartiles for this distribution.
	StandardDeviation	Gets the Standard Deviation (the square root of the variance) for the current distribution.
	Support	Gets the support interval for this distribution.
	Variance	Gets the variance for this distribution.

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Methods

	Name	Description
	BaseDistributionFunction	Computes the cumulative distribution function by summing the outputs of the ProbabilityMassFunction(Int32) for all elements in the distribution domain. Note that this method should not be used in case there is a more efficient formula for computing the CDF of a distribution.
	BaseInverseDistributionFunction	Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p using a numerical approximation based on binary search.
	Clone	Creates a new object that is a copy of the current instance. (Inherited from DistributionBase.)
	ComplementaryDistributionFunction(Int32)	Gets P(X > k) the complementary cumulative distribution function (ccdf) for this distribution evaluated at point k. This function is also known as the Survival function.
	ComplementaryDistributionFunction(Int32, Boolean)	Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point k. This function is also known as the Survival function.
	CumulativeHazardFunction	Gets the cumulative hazard function for this distribution evaluated at point x.
	DistributionFunction(Int32)	Gets P(X ≤ k), the cumulative distribution function (cdf) for this distribution evaluated at point k.
	DistributionFunction(Int32, Boolean)	Gets P(X ≤ k) or P(X < k), the cumulative distribution function (cdf) for this distribution evaluated at point k, depending on the value of the inclusive parameter.
	DistributionFunction(Int32, Int32)	Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b).
	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.
	Fit(Int32)	Fits the underlying distribution to a given set of observations.
	Fit(Double, IFittingOptions)	Fits the underlying distribution to a given set of observations.
	Fit(Double, Double)	Fits the underlying distribution to a given set of observations.
	Fit(Double, Int32)	Fits the underlying distribution to a given set of observations.
	Fit(Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations.
	Fit(Double, Double, IFittingOptions)	Fits the underlying distribution to a given set of observations.
	Fit(Double, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations.
	Fit(Int32, Double, IFittingOptions)	Fits the underlying distribution to a given set of observations.
	Fit(Int32, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations.
	Generate	Generates a random observation from the current distribution.
	Generate(Int32)	Generates a random vector of observations from the current distribution.
	Generate(Random)	Generates a random observation from the current distribution.
	Generate(Int32, Double)	Generates a random vector of observations from the current distribution.
	Generate(Int32, Int32)	Generates a random vector of observations from the current distribution.
	Generate(Int32, Random)	Generates a random vector of observations from the current distribution.
	Generate(Int32, Double, Random)	Generates a random vector of observations from the current distribution.
	Generate(Int32, Int32, Random)	Generates a random vector of observations from the current distribution.
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRange	Gets the distribution range within a given percentile.
	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.
	InnerComplementaryDistributionFunction	Gets P(X > k) the complementary cumulative distribution function (ccdf) for this distribution evaluated at point k. This function is also known as the Survival function.
	InnerDistributionFunction	Gets P(X ≤ k), the cumulative distribution function (cdf) for this distribution evaluated at point k.
	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.
	InnerLogProbabilityMassFunction	Gets the log-probability mass function (pmf) for this distribution evaluated at point x.
	InnerProbabilityMassFunction	Gets the probability mass function (pmf) for this distribution evaluated at point x.
	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.
	LogCumulativeHazardFunction	Gets the log-cumulative hazard function for this distribution evaluated at point x.
	LogProbabilityMassFunction	Gets the log-probability mass function (pmf) for this distribution evaluated at point x.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ProbabilityMassFunction	Gets the probability mass function (pmf) for this distribution evaluated at point x.
	QuantileDensityFunction	Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
	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. (Inherited from DistributionBase.)

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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

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

Reference

Accord.Statistics.Distributions.Univariate Namespace

Accord.Statistics.Distributions.UnivariateBernoulliDistribution

Accord.Statistics.Distributions.UnivariateGeometricDistribution

Accord.Statistics.Distributions.UnivariatePoissonDistribution

Inheritance Hierarchy