Package com.imsl.stat.distributions

Class ExtremeValuePD

java.lang.Object
com.imsl.stat.distributions.ProbabilityDistribution
com.imsl.stat.distributions.ExtremeValuePD
All Implemented Interfaces:
com.imsl.stat.distributions.MethodOfMomentsInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable
public class ExtremeValuePD extends ProbabilityDistribution implements Serializable, Cloneable, com.imsl.stat.distributions.MethodOfMomentsInterface, PDFHessianInterface
The extreme value/Gumbel probability distribution.
See Also:

  • Constructor Details

    • ExtremeValuePD

      public ExtremeValuePD()
      Constructor for the extreme value/Gumbel probability distribution.

  • Method Details

    • 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