com.imsl.stat.distributions

Class GeneralizedGaussianPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.GeneralizedGaussianPD

All Implemented Interfaces:

Serializable, Cloneable

public class GeneralizedGaussianPD
extends ProbabilityDistribution
implements Serializable, Cloneable

The generalized Gaussian probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
GeneralizedGaussianPD() Constructs a generalized Gaussian probability distribution.

Method Summary

Modifier and Type	Method and Description
double[]	getParameterLowerBounds() Returns the lower bounds of the parameters.
double[]	getParameterUpperBounds() Returns the upper bounds of the parameters.
double	pdf(double x, double... params) Returns the value of the generalized Gaussian probability density function.

Methods inherited from class com.imsl.stat.distributions.ProbabilityDistribution

getNumberOfParameters, getPDFGradientApproximation, getPDFHessianApproximation, getRangeOfX, setRangeOfX

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GeneralizedGaussianPD

public GeneralizedGaussianPD()

Constructs a generalized Gaussian probability distribution.

Method Detail

getParameterLowerBounds

public double[] getParameterLowerBounds()

Returns the lower bounds of the parameters.

Specified by:

getParameterLowerBounds in class ProbabilityDistribution

Returns:

a double array containing the lower bounds for \(\mu\in\mathbb{R}\), \(\alpha \gt 0\), and \(\beta \gt 0\)

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bounds of the parameters.

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array containing the upper bounds for \(\mu\in\mathbb{R}\), \(\alpha \gt 0\), and \(\beta \gt 0\)

pdf

public double pdf(double x,
                  double... params)

Returns the value of the generalized Gaussian probability density function.

The probability density function of the generalized Gaussian distribution is

$$ f(x; \mu,\alpha, \beta) = \frac{\beta}{2\alpha\Gamma(\frac{1}{\beta})} e^{-(\frac{|x-\mu|}{\alpha})^\beta} $$

where \(\mu\in\mathbb{R}\) is the location parameter, \(\alpha \gt 0\) is the scale parameter, and \(\beta \gt 0\) is the shape parameter. Note that this follows the parameterization given in Wikipedia. There are alternative parameterizations, as in Roenko, et. al. 2014.

References
1. Roenko, Alexey, Lukin, Vladimir, Djurovic, Igor, Simeunović, Marko. (2014). Estimation of parameters for generalized Gaussian distribution. ISCCSP 2014 - 2014 6th International Symposium on Communications, Control and Signal Processing, Proceedings. 376-379.
2. Wikipedia contributors. "Generalized normal distribution." Wikipedia, The Free Encyclopedia.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

x - a double, the value (quantile) at which to evaluate the pdf

params - a double array containing \(\mu\), \(\alpha\), and \(\beta\). The parameters can also be given in the form pdf(x,a,b,c), where a=\(\mu\), b=\(\alpha\), and c=\(\beta\) are scalars.

Returns:

a double, the probability density at x given the parameter values