GompertzDistribution Class

SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateGompertzDistribution

public class GompertzDistribution : UnivariateContinuousDistribution

Public Class GompertzDistribution
	Inherits UnivariateContinuousDistribution

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	Name	Description
	GompertzDistribution	Initializes a new instance of the GompertzDistribution class.

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	Name	Description
	Entropy	Not supported. (Overrides UnivariateContinuousDistributionEntropy.)
	Mean	Not supported. (Overrides UnivariateContinuousDistributionMean.)
	Median	Gets the median for this distribution. (Overrides UnivariateContinuousDistributionMedian.)
	Mode	Gets the mode for this distribution. (Overrides UnivariateContinuousDistributionMode.)
	Quartiles	Gets the Quartiles for this distribution. (Inherited from UnivariateContinuousDistribution.)
	StandardDeviation	Gets the Standard Deviation (the square root of the variance) for the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Support	Gets the support interval for this distribution. (Overrides UnivariateContinuousDistributionSupport.)
	Variance	Not supported. (Overrides UnivariateContinuousDistributionVariance.)

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	Name	Description
	Clone	Creates a new object that is a copy of the current instance. (Overrides DistributionBaseClone.)
	ComplementaryDistributionFunction	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.)
	CumulativeHazardFunction	Gets the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(Double)	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(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.)
	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 UnivariateContinuousDistribution.)
	Fit(Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Generate	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Random)	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRange	Gets the distribution range within a given percentile. (Inherited from UnivariateContinuousDistribution.)
	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 UnivariateContinuousDistribution.)
	InnerComplementaryDistributionFunction	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.)
	InnerDistributionFunction	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
	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. (Inherited from UnivariateContinuousDistribution.)
	InnerLogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
	InnerProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
	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 UnivariateContinuousDistribution.)
	LogCumulativeHazardFunction	Gets the log of the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	LogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	QuantileDensityFunction	Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p. (Inherited from UnivariateContinuousDistribution.)
	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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The Gompertz distribution is a continuous probability distribution. The Gompertz distribution is often applied to describe the distribution of adult lifespans by demographers and actuaries. Related fields of science such as biology and gerontology also considered the Gompertz distribution for the analysis of survival. More recently, computer scientists have also started to model the failure rates of computer codes by the Gompertz distribution. In marketing science, it has been used as an individual-level model of customer lifetime.

References:

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

The following example shows how to construct a Gompertz distribution with η = 4.2 and b = 1.1.

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// Create a new Gompertz distribution with η = 4.2 and b = 1.1
GompertzDistribution dist = new GompertzDistribution(eta: 4.2, b: 1.1);

// Common measures
double median = dist.Median; // 0.13886469671401389

// Cumulative distribution functions
double cdf = dist.DistributionFunction(x: 0.27); // 0.76599768199799145
double ccdf = dist.ComplementaryDistributionFunction(x: 0.27); // 0.23400231800200855
double icdf = dist.InverseDistributionFunction(p: cdf); // 0.26999999999766749

// Probability density functions
double pdf = dist.ProbabilityDensityFunction(x: 0.27); // 1.4549484164912097
double lpdf = dist.LogProbabilityDensityFunction(x: 0.27); // 0.37497044741163688

// Hazard (failure rate) functions
double hf = dist.HazardFunction(x: 0.27); // 6.2176666834502088
double chf = dist.CumulativeHazardFunction(x: 0.27); // 1.4524242576820101

// String representation
string str = dist.ToString(CultureInfo.InvariantCulture); // "Gompertz(x; η = 4.2, b = 1.1)"

Reference

Accord.Statistics.Distributions.Univariate Namespace