GeneralDiscreteDistribution Class 
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public sealed class GeneralDiscreteDistribution : UnivariateDiscreteDistribution, IUnivariateFittableDistribution, IFittableDistribution<double>, IFittable<double>, IDistribution<double>, IDistribution, ICloneable, IUnivariateDistribution<double>, IUnivariateDistribution, IFittableDistribution<double, GeneralDiscreteOptions>, IFittable<double, GeneralDiscreteOptions>, IFittableDistribution<double[], GeneralDiscreteOptions>, IFittable<double[], GeneralDiscreteOptions>, IFittable<double[]>, IFittableDistribution<double[]>, IDistribution<double[]>, IFittableDistribution<int, GeneralDiscreteOptions>, IFittable<int, GeneralDiscreteOptions>, IFittable<int>, IFittableDistribution<int>, IDistribution<int>, ISampleableDistribution<int>, IRandomNumberGenerator<int>, ISampleableDistribution<double>, IRandomNumberGenerator<double>
The GeneralDiscreteDistribution type exposes the following members.
Name  Description  

GeneralDiscreteDistribution(Double) 
Constructs a new generic discrete distribution.
 
GeneralDiscreteDistribution(Boolean, Double) 
Constructs a new generic discrete distribution.
 
GeneralDiscreteDistribution(Int32, Boolean) 
Constructs a new uniform discrete distribution.
 
GeneralDiscreteDistribution(Int32, Double) 
Constructs a new generic discrete distribution.
 
GeneralDiscreteDistribution(Int32, Int32, Boolean) 
Constructs a new uniform discrete distribution.

Name  Description  

Entropy 
Gets the entropy for this distribution.
(Overrides UnivariateDiscreteDistributionEntropy.)  
Frequencies 
Gets the probabilities associated with each discrete variable value.
Note: if the frequencies in this property are manually changed, the
rest of the class properties (Mode, Mean, ...) will not be automatically
updated to reflect the actual inserted values.
 
Item 
Gets the probability value associated with the symbol i.
 
Length 
Gets the number of symbols in the distribution.
 
Maximum 
Gets the integer value where the
discrete distribution ends.
 
Mean 
Gets the mean for this distribution.
(Overrides UnivariateDiscreteDistributionMean.)  
Median 
Gets the median for this distribution.
(Inherited from UnivariateDiscreteDistribution.)  
Minimum 
Gets the integer value where the
discrete distribution starts.
 
Mode 
Gets the mode for this distribution.
(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.)  
Variance 
Gets the variance for this distribution.
(Overrides UnivariateDiscreteDistributionVariance.) 
Name  Description  

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 the probability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateDiscreteDistributionDistributionFunction(Int32).)  
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 semiclosed 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.)  
Fit(Double) 
Fits the underlying distribution to a given set of observations.
 
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, Double) 
Fits the underlying distribution to a given set of observations.
 
Fit(Int32, Double) 
Fits the underlying distribution to a given set of observations.
 
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, GeneralDiscreteOptions) 
Fits the underlying distribution to a given set of observations.
 
Fit(Double, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateDiscreteDistributionFit(Double, Double, IFittingOptions).)  
Fit(Double, Double, GeneralDiscreteOptions) 
Fits the underlying distribution to a given set of observations.
 
Fit(Int32, Double, GeneralDiscreteOptions) 
Fits the underlying distribution to a given set of observations.
 
Fit(Int32, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateDiscreteDistributionFit(Int32, Double, IFittingOptions).)  
Fit(Double, Int32, 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.)  
FromMatrix(Double, Boolean) 
Creates general discrete distributions given a matrix of symbol probabilities.
 
FromMatrix(Double, Boolean) 
Creates general discrete distributions given a matrix of symbol probabilities.
 
Generate 
Generates a random observation from the current distribution.
(Overrides UnivariateDiscreteDistributionGenerate.)  
Generate(Int32) 
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.
(Overrides UnivariateDiscreteDistributionGenerate(Int32, Int32).)  
Generate(Int32, Double) 
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.)  
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 logcumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateDiscreteDistribution.)  
LogProbabilityMassFunction 
Gets the logprobability mass function (pmf) for
this distribution evaluated at point x.
(Overrides UnivariateDiscreteDistributionLogProbabilityMassFunction(Int32).)  
ProbabilityMassFunction 
Gets the probability mass function (pmf) for
this distribution evaluated at point x.
(Overrides UnivariateDiscreteDistributionProbabilityMassFunction(Int32).)  
QuantileDensityFunction 
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateDiscreteDistribution.)  
Random(Double, Boolean) 
Returns a random symbol within the given symbol probabilities.
 
Random(Double, Int32) 
Returns a random sample within the given symbol probabilities.
 
Random(Double, Int32, Int32, Boolean) 
Returns a random sample within the given symbol probabilities.
 
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).)  
Uniform 
Constructs a new uniform discrete distribution.

Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(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.)  
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 Matrix.) 
An univariate categorical distribution is a statistical distribution whose variables can take on only discrete values. Each discrete value defined within the interval of the distribution has an associated probability value indicating its frequency of occurrence.
The discrete uniform distribution is a special case of a generic discrete distribution whose probability values are constant.
// Create a Categorical distribution for 3 symbols, in which // the first and second symbol have 25% chance of appearing, // and the third symbol has 50% chance of appearing. // 1st 2nd 3rd double[] probabilities = { 0.25, 0.25, 0.50 }; // Create the categorical with the given probabilities var dist = new GeneralDiscreteDistribution(probabilities); // Common measures double mean = dist.Mean; // 1.25 double median = dist.Median; // 1.00 double var = dist.Variance; // 0.6875 // Cumulative distribution functions double cdf = dist.DistributionFunction(k: 2); // 1.0 double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.0 // Probability mass functions double pdf1 = dist.ProbabilityMassFunction(k: 0); // 0.25 double pdf2 = dist.ProbabilityMassFunction(k: 1); // 0.25 double pdf3 = dist.ProbabilityMassFunction(k: 2); // 0.50 double lpdf = dist.LogProbabilityMassFunction(k: 2); // 0.69314718055994529 // Quantile function int icdf1 = dist.InverseDistributionFunction(p: 0.17); // 0 int icdf2 = dist.InverseDistributionFunction(p: 0.39); // 1 int icdf3 = dist.InverseDistributionFunction(p: 0.56); // 2 // Hazard (failure rate) functions double hf = dist.HazardFunction(x: 0); // 0.33333333333333331 double chf = dist.CumulativeHazardFunction(x: 0); // 0.2876820724517809 // String representation string str = dist.ToString(CultureInfo.InvariantCulture); // "Categorical(x; p = { 0.25, 0.25, 0.5 })"