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KumaraswamyDistribution Class |
Kumaraswamy distribution.
Inheritance HierarchySystemObject
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateKumaraswamyDistribution
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateKumaraswamyDistribution
Namespace: Accord.Statistics.Distributions.Univariate
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax[SerializableAttribute] public class KumaraswamyDistribution : UnivariateContinuousDistribution
The KumaraswamyDistribution type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | KumaraswamyDistribution |
Constructs a new Kumaraswamy's double bounded distribution with
the given two non-negative shape parameters a and b.
|
Properties| Name | Description | |
|---|---|---|
 | A |
Gets the distribution's non-negative shape parameter a.
|
| B |
Gets the distribution's non-negative shape parameter b.
|
| Entropy |
Not supported.
(Overrides UnivariateContinuousDistributionEntropy.) |
| Mean |
Gets the mean for this distribution.
(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 |
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.) |
Methods| 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.
(Inherited from UnivariateContinuousDistribution.) |
| 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).) |
Extension Methods| 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.) |
RemarksIn probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval [0,1] differing in the values of their two non-negative shape parameters, a and b. It is similar to the Beta distribution, but much simpler to use especially in simulation studies due to the simple closed form of both its probability density function and cumulative distribution function. This distribution was originally proposed by Poondi Kumaraswamy for variables that are lower and upper bounded.
A good example of the use of the Kumaraswamy distribution is the storage volume of a reservoir of capacity zmax whose upper bound is zmax and lower bound is 0 (Fletcher and Ponnambalam, 1996).
References:
ExamplesThe following example shows how to create and test the main characteristics of an Kumaraswamy distribution given its two non-negative shape parameters:
// Create a new Kumaraswamy distribution with shape (4,2) var kumaraswamy = new KumaraswamyDistribution(a: 4, b: 2); double mean = kumaraswamy.Mean; // 0.71111111111111114 double median = kumaraswamy.Median; // 0.73566031573423674 double mode = kumaraswamy.Mode; // 0.80910671157022118 double var = kumaraswamy.Variance; // 0.027654320987654302 double cdf = kumaraswamy.DistributionFunction(x: 0.4); // 0.050544639999999919 double pdf = kumaraswamy.ProbabilityDensityFunction(x: 0.4); // 0.49889280000000014 double lpdf = kumaraswamy.LogProbabilityDensityFunction(x: 0.4); // -0.69536403596913343 double ccdf = kumaraswamy.ComplementaryDistributionFunction(x: 0.4); // 0.94945536000000008 double icdf = kumaraswamy.InverseDistributionFunction(p: cdf); // 0.40000011480618253 double hf = kumaraswamy.HazardFunction(x: 0.4); // 0.52545155993431869 double chf = kumaraswamy.CumulativeHazardFunction(x: 0.4); // 0.051866764053008864 string str = kumaraswamy.ToString(CultureInfo.InvariantCulture); // Kumaraswamy(x; a = 4, b = 2)
See Also