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ExponentialDistribution Class

Exponential distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateExponentialDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.5.0
Syntax
[SerializableAttribute]
public class ExponentialDistribution : UnivariateContinuousDistribution, 
	IFittableDistribution<double, IFittingOptions>, IFittable<double, IFittingOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable, ISampleableDistribution<double>, IRandomNumberGenerator<double>
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The ExponentialDistribution type exposes the following members.

Constructors
  NameDescription
Public methodExponentialDistribution
Creates a new Exponential distribution with the given rate.
Public methodExponentialDistribution(Double)
Creates a new Exponential distribution with the given rate.
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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.
(Overrides UnivariateContinuousDistributionMedian.)
Public propertyMode
Gets the mode for this distribution.
(Overrides UnivariateContinuousDistributionMode.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyRate
Gets the distribution's rate parameter lambda (λ).
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.)
Public methodStatic memberEstimate(Double)
Estimates a new Exponential distribution from a given set of observations.
Public methodStatic memberEstimate(Double, Double)
Estimates a new Exponential distribution from a given set of observations.
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 methodCode exampleFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
Public methodFit(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.
(Overrides UnivariateContinuousDistributionGenerate.)
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.
(Overrides UnivariateContinuousDistributionGenerate(Int32, Double).)
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.
(Overrides UnivariateContinuousDistributionInverseDistributionFunction(Double).)
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.
(Overrides UnivariateContinuousDistributionLogProbabilityDensityFunction(Double).)
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 methodStatic memberRandom(Double)
Generates a random observation from the Exponential distribution with the given parameters.
Public methodStatic memberRandom(Double, Int32)
Generates a random vector of observations from the Exponential distribution with the given parameters.
Public methodStatic memberRandom(Double, Int32, Double)
Generates a random vector of observations from the Exponential distribution with the given parameters.
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 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

In probability theory and statistics, the exponential distribution (a.k.a. negative exponential distribution) is a family of continuous probability distributions. It describes the time between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate. It is the continuous analogue of the geometric distribution.

Note that the exponential distribution is not the same as the class of exponential families of distributions, which is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes the normal distribution, binomial distribution, gamma distribution, Poisson, and many others.

References:

Examples

The following example shows how to create and test the main characteristics of an Exponential distribution given a lambda (λ) rate of 0.42:

// Create an Exponential distribution with λ = 0.42
var exp = new ExponentialDistribution(rate: 0.42);

// Common measures
double mean = exp.Mean;     // 2.3809523809523809
double median = exp.Median; // 1.6503504299046317
double var = exp.Variance;  // 5.6689342403628125

// Cumulative distribution functions
double cdf  = exp.DistributionFunction(x: 0.27);          // 0.10720652870550407
double ccdf = exp.ComplementaryDistributionFunction(x: 0.27); // 0.89279347129449593
double icdf = exp.InverseDistributionFunction(p: cdf);        // 0.27

// Probability density functions
double pdf  = exp.ProbabilityDensityFunction(x: 0.27);    // 0.3749732579436883
double lpdf = exp.LogProbabilityDensityFunction(x: 0.27); // -0.98090056770472311

// Hazard (failure rate) functions
double hf = exp.HazardFunction(x: 0.27);            // 0.42
double chf = exp.CumulativeHazardFunction(x: 0.27); // 0.1134

// String representation
string str = exp.ToString(CultureInfo.InvariantCulture); // Exp(x; λ = 0.42)

The following example shows how to generate random samples drawn from an Exponential distribution and later how to re-estimate a distribution from the generated samples.

// Create an Exponential distribution with λ = 2.5
var exp = new ExponentialDistribution(rate: 2.5);

// Generate a million samples from this distribution:
double[] samples = target.Generate(1000000);

// Create a default exponential distribution
var newExp = new ExponentialDistribution();

// Fit the samples
newExp.Fit(samples);

// Check the estimated parameters
double rate = newExp.Rate; // 2.5
See Also