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Accord.NET (logo) GeneralContinuousDistribution Class
General continuous distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateGeneralContinuousDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.4.0
Syntax
public class GeneralContinuousDistribution : UnivariateContinuousDistribution
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The GeneralContinuousDistribution type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyEntropy
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.)
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.
(Overrides UnivariateContinuousDistributionMode.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
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.
(Overrides UnivariateContinuousDistributionDistributionFunction(Double).)
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 methodStatic memberFromDensityFunction(FuncDouble, Double)
Creates a new GeneralContinuousDistribution using only a probability density function definition.
Public methodStatic memberFromDensityFunction(DoubleRange, FuncDouble, Double)
Creates a new GeneralContinuousDistribution using only a probability density function definition.
Public methodStatic memberFromDensityFunction(DoubleRange, FuncDouble, Double, IUnivariateIntegration)
Creates a new GeneralContinuousDistribution using only a probability density function definition.
Public methodStatic memberFromDistribution
Creates a new GeneralContinuousDistribution from an existing continuous distribution.
Public methodStatic memberFromDistributionFunction(FuncDouble, Double)
Creates a new GeneralContinuousDistribution using only a cumulative distribution function definition.
Public methodStatic memberFromDistributionFunction(DoubleRange, FuncDouble, Double)
Creates a new GeneralContinuousDistribution using only a cumulative distribution function definition.
Public methodStatic memberFromDistributionFunction(DoubleRange, FuncDouble, Double, IUnivariateIntegration)
Creates a new GeneralContinuousDistribution using only a cumulative distribution function definition.
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(Int32, Double)
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.)
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.
(Overrides UnivariateContinuousDistributionProbabilityDensityFunction(Double).)
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 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.)
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 Matrix.)
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Remarks

The general continuous distribution provides the automatic calculation for a variety of distribution functions and measures given only definitions for the Probability Density Function (PDF) or the Cumulative Distribution Function (CDF). Values such as the Expected value, Variance, Entropy and others are computed through numeric integration.

Examples
// Let's suppose we have a formula that defines a probability distribution
// but we dont know much else about it. We don't know the form of its cumulative
// distribution function, for example. We would then like to know more about
// it, such as the underlying distribution's moments, characteristics, and 
// properties.

// Let's suppose the formula we have is this one:
double mu = 5;
double sigma = 4.2;

Func>double, double> df = x => 1.0 / (sigma * Math.Sqrt(2 * Math.PI))
                * Math.Exp(-Math.Pow(x - mu, 2) / (2 * sigma * sigma));

// And for the moment, let's also pretend we don't know it is actually the
// p.d.f. of a Gaussian distribution with mean 5 and std. deviation of 4.2.

// So, let's create a distribution based _solely_ on the formula we have:
var distribution = GeneralContinuousDistribution.FromDensityFunction(df);

// Now, we can check everything that we can know about it:

double mean = distribution.Mean;     // 5      (note that all of those have been
double median = distribution.Median; // 5       detected automatically simply from
double var = distribution.Variance;  // 17.64   the given density formula through
double mode = distribution.Mode;     // 5       numerical methods)

double cdf = distribution.DistributionFunction(x: 1.4);           // 0.19568296915377595
double pdf = distribution.ProbabilityDensityFunction(x: 1.4);     // 0.065784567984404935
double lpdf = distribution.LogProbabilityDensityFunction(x: 1.4); // -2.7213699972695058

double ccdf = distribution.ComplementaryDistributionFunction(x: 1.4); // 0.80431703084622408
double icdf = distribution.InverseDistributionFunction(p: cdf);       // 1.3999999997024655

double hf = distribution.HazardFunction(x: 1.4);            // 0.081789351041333558
double chf = distribution.CumulativeHazardFunction(x: 1.4); // 0.21776177055276186
See Also