GeneralizedNormalDistribution Class |
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public class GeneralizedNormalDistribution : UnivariateContinuousDistribution
The GeneralizedNormalDistribution type exposes the following members.
Name | Description | |
---|---|---|
GeneralizedNormalDistribution |
Constructs a Generalized Normal distribution with the given parameters.
|
Name | Description | |
---|---|---|
Entropy |
Gets the Entropy for this Normal distribution.
(Overrides UnivariateContinuousDistributionEntropy.) | |
Mean |
Gets the location value μ (mu) for the 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.) |
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 the
Generalized Normal 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
the Normal 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.) | |
Laplace |
Create an LaplaceDistribution distribution using a
GeneralizedNormalDistribution specialization.
| |
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.) | |
Normal |
Create an NormalDistribution distribution using a
GeneralizedNormalDistribution specialization.
| |
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).) |
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.) |
The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "version 1" and "version 2". However this is not a standard nomenclature.
Known also as the exponential power distribution, or the generalized error distribution, this is a parametric family of symmetric distributions. It includes all normal and Laplace distributions, and as limiting cases it includes all continuous uniform distributions on bounded intervals of the real line.
References:
This examples shows how to create a Generalized normal distribution and compute some of its properties.
// Creates a new generalized normal distribution with the given parameters var normal = new GeneralizedNormalDistribution(location: 1, scale: 5, shape: 0.42); double mean = normal.Mean; // 1 double median = normal.Median; // 1 double mode = normal.Mode; // 1 double var = normal.Variance; // 19200.781700666659 double cdf = normal.DistributionFunction(x: 1.4); // 0.51076148867681703 double pdf = normal.ProbabilityDensityFunction(x: 1.4); // 0.024215092283124507 double lpdf = normal.LogProbabilityDensityFunction(x: 1.4); // -3.7207791921441378 double ccdf = normal.ComplementaryDistributionFunction(x: 1.4); // 0.48923851132318297 double icdf = normal.InverseDistributionFunction(p: cdf); // 1.4000000149740108 double hf = normal.HazardFunction(x: 1.4); // 0.049495474543966168 double chf = normal.CumulativeHazardFunction(x: 1.4); // 0.7149051552030572 string str = normal.ToString(CultureInfo.InvariantCulture); // GGD(x; μ = 1, α = 5, β = 0.42)