Click or drag to resize
Accord.NET (logo) GompertzDistribution Class
Gompertz distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateGompertzDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.4.0
Syntax
public class GompertzDistribution : UnivariateContinuousDistribution
Request Example View Source

The GompertzDistribution type exposes the following members.

Constructors
  NameDescription
Public methodGompertzDistribution
Initializes a new instance of the GompertzDistribution class.
Top
Properties
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 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.
(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 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).)
Top
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.)
Top
Remarks

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:

Examples

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

// 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)"
See Also