com.imsl.stat.distributions

Class ExtremeValuePD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.ExtremeValuePD

All Implemented Interfaces:

PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

public class ExtremeValuePD
extends ProbabilityDistribution
implements Serializable, Cloneable, PDFHessianInterface

The extreme value/Gumbel probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
ExtremeValuePD() Constructor for the extreme value/Gumbel 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[]	getPDFGradient(double x, double... params) Returns the analytic gradient of the pdf.
double[][]	getPDFHessian(double x, double... params) Returns the analytic Hessian of the pdf.
double	pdf(double x, double... params) Returns the value of the extreme value 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

ExtremeValuePD

public ExtremeValuePD()

Constructor for the extreme value/Gumbel 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 of length 2 containing the lower bounds for \(\mu \in\mathbb{R}\) and \(\beta>0\)

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bounds of the parameters.

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array of length 2 containing the upper bounds for \(\mu \in\mathbb{R}\) and \(\beta>0\)

pdf

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

Returns the value of the extreme value probability density function.

The probability density function of the extreme value distribution is $$f(x;\mu,\beta)=\frac{1}{\beta}e^{\frac{x-\mu}{\beta}}\exp\left(-e^{\frac{x-\mu}{\beta}}\right)$$ where \(\mu \in\mathbb{R}\) is the location parameter and \(\beta>0\) is the scale parameter.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

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

params - a double array containing the parameters, with params[0]=\(\mu\) and params[1]=\(\beta\). The parameters can also be given in the form pdf(x,a,b), where a=\(\mu\) and b=\(\beta\) are scalars.

Returns:

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

getPDFHessian

public double[][] getPDFHessian(double x,
                                double... params)

Returns the analytic Hessian of the pdf.

Specified by:

getPDFHessian in interface PDFHessianInterface

Parameters:

x - a double, the value at which to evaluate the Hessian

params - a double array containing values of the parameters

Returns:

a double matrix containing the second partial derivatives of the pdf with respect to the parameters

getPDFGradient

public double[] getPDFGradient(double x,
                               double... params)

Returns the analytic gradient of the pdf.

Specified by:

getPDFGradient in interface PDFGradientInterface

Parameters:

x - a double, the value at which to evaluate the gradient

params - a double array containing values of the parameters

Returns:

a double array containing the first partial derivative of the pdf with respect to the parameters