DegenerateDistribution Class

SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateDiscreteDistribution
      Accord.Statistics.Distributions.UnivariateDegenerateDistribution

[SerializableAttribute]
public class DegenerateDistribution : UnivariateDiscreteDistribution

<SerializableAttribute>
Public Class DegenerateDistribution
	Inherits UnivariateDiscreteDistribution

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	Name	Description
	DegenerateDistribution	Initializes a new instance of the DegenerateDistribution class.
	DegenerateDistribution(Int32)	Initializes a new instance of the DegenerateDistribution class.

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	Name	Description
	Entropy	Gets the entropy for this distribution, which is zero. (Overrides UnivariateDiscreteDistributionEntropy.)
	Mean	Gets the mean for this distribution. (Overrides UnivariateDiscreteDistributionMean.)
	Median	Gets the median for this distribution, which should equal Value. (Overrides UnivariateDiscreteDistributionMedian.)
	Mode	Gets the mode for this distribution, which should equal Value. (Overrides UnivariateDiscreteDistributionMode.)
	Quartiles	Gets the Quartiles for this distribution. (Inherited from UnivariateDiscreteDistribution.)
	StandardDeviation	Gets the Standard Deviation (the square root of the variance) for the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Support	Gets the support interval for this distribution. (Overrides UnivariateDiscreteDistributionSupport.)
	Value	Gets the unique value whose probability is different from zero.
	Variance	Gets the variance for this distribution, which should equal 0. (Overrides UnivariateDiscreteDistributionVariance.)

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	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. (Inherited from UnivariateDiscreteDistribution.)
	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. (Inherited from UnivariateDiscreteDistribution.)
	Clone	Creates a new object that is a copy of the current instance. (Overrides DistributionBaseClone.)
	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. (Inherited from UnivariateDiscreteDistribution.)
	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. (Inherited from UnivariateDiscreteDistribution.)
	CumulativeHazardFunction	Gets the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateDiscreteDistribution.)
	DistributionFunction(Int32)	Gets P(X ≤ k), the cumulative distribution function (cdf) for this distribution evaluated at point k. (Inherited from UnivariateDiscreteDistribution.)
	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. (Inherited from UnivariateDiscreteDistribution.)
	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). (Inherited from UnivariateDiscreteDistribution.)
	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 UnivariateDiscreteDistribution.)
	Fit(Int32)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Double, Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Double, Int32)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Double, Double, IFittingOptions)	The DegenerateDistribution does not support fitting. (Overrides UnivariateDiscreteDistributionFit(Double, Double, IFittingOptions).)
	Fit(Double, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Int32, Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Fit(Int32, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateDiscreteDistribution.)
	Generate	Generates a random observation from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Int32)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Random)	Generates a random observation from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Int32, Double)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Int32, Int32)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Int32, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Int32, Double, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	Generate(Int32, Int32, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateDiscreteDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRange	Gets the distribution range within a given percentile. (Inherited from UnivariateDiscreteDistribution.)
	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 UnivariateDiscreteDistribution.)
	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. (Inherited from UnivariateDiscreteDistribution.)
	InnerDistributionFunction	Gets the cumulative distribution function (cdf) for this distribution evaluated at point k. (Overrides UnivariateDiscreteDistributionInnerDistributionFunction(Int32).)
	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. (Overrides UnivariateDiscreteDistributionInnerInverseDistributionFunction(Double).)
	InnerLogProbabilityMassFunction	Gets the log-probability mass function (pmf) for this distribution evaluated at point x. (Inherited from UnivariateDiscreteDistribution.)
	InnerProbabilityMassFunction	Gets the probability mass function (pmf) for this distribution evaluated at point x. (Overrides UnivariateDiscreteDistributionInnerProbabilityMassFunction(Int32).)
	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 UnivariateDiscreteDistribution.)
	LogCumulativeHazardFunction	Gets the log-cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateDiscreteDistribution.)
	LogProbabilityMassFunction	Gets the log-probability mass function (pmf) for this distribution evaluated at point x. (Inherited from UnivariateDiscreteDistribution.)
	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. (Inherited from UnivariateDiscreteDistribution.)
	QuantileDensityFunction	Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p. (Inherited from UnivariateDiscreteDistribution.)
	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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	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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In mathematics, a degenerate distribution or deterministic distribution is the probability distribution of a random variable which only takes a single value. Examples include a two-headed coin and rolling a die whose sides all show the same number. While this distribution does not appear random in the everyday sense of the word, it does satisfy the definition of random variable.

The degenerate distribution is localized at a point k0 on the real line. The probability mass function is a Delta function at k0.

References:

Wikipedia, The Free Encyclopedia. Degenerate distribution. Available on: http://en.wikipedia.org/wiki/Degenerate_distribution

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

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var dist = new DegenerateDistribution(value: 2);

double mean = dist.Mean;     // 2
double median = dist.Median; // 2
double mode = dist.Mode;     // 2
double var = dist.Variance;  // 1

double cdf1 = dist.DistributionFunction(k: 1);    // 0
double cdf2 = dist.DistributionFunction(k: 2);   // 1

double pdf1 = dist.ProbabilityMassFunction(k: 1); // 0
double pdf2 = dist.ProbabilityMassFunction(k: 2); // 1
double pdf3 = dist.ProbabilityMassFunction(k: 3); // 0

double lpdf = dist.LogProbabilityMassFunction(k: 2); // 0
double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.0

int icdf1 = dist.InverseDistributionFunction(p: 0.0); // 1
int icdf2 = dist.InverseDistributionFunction(p: 0.5); // 3
int icdf3 = dist.InverseDistributionFunction(p: 1.0); // 2

double hf = dist.HazardFunction(x: 0); // 0.0
double chf = dist.CumulativeHazardFunction(x: 0); // 0.0

string str = dist.ToString(CultureInfo.InvariantCulture); // Degenerate(x; k0 = 2)

Reference

Accord.Statistics.Distributions.Univariate Namespace