Class GeneralizedExtremeValueDistribution

  • All Implemented Interfaces:
    Distribution

    public class GeneralizedExtremeValueDistribution
    extends java.lang.Object
    implements Distribution
    Generalized Extreme Value (GEV) distribution, also known as Fisher–Tippett distribution.

    This is a generalization of the Frechnet, Gumbel and (reversed) Weibull distributions.

    Implementation notice: In ELKI 0.8.0, the sign of the shape was negated.

    Since:
    0.6.0
    Author:
    Erich Schubert
    • Field Summary

      Fields 
      Modifier and Type Field Description
      (package private) double k
      Parameters (location, scale, shape)
      (package private) double mu
      Parameters (location, scale, shape)
      (package private) double sigma
      Parameters (location, scale, shape)
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double cdf​(double val)
      Return the cumulative density function at the given value.
      static double cdf​(double val, double mu, double sigma, double k)
      CDF of GEV distribution
      double getK()
      Get the k parameter.
      double getMu()
      Get location.
      double getSigma()
      Get sigma.
      double logpdf​(double x)
      Return the log density of an existing value
      static double logpdf​(double x, double mu, double sigma, double k)
      log PDF of GEV distribution
      double pdf​(double x)
      Return the density of an existing value
      static double pdf​(double x, double mu, double sigma, double k)
      PDF of GEV distribution
      double quantile​(double val)
      Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
      static double quantile​(double val, double mu, double sigma, double k)
      Quantile function of GEV distribution
      java.lang.String toString()
      Describe the distribution
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
    • Field Detail

      • mu

        final double mu
        Parameters (location, scale, shape)
      • sigma

        final double sigma
        Parameters (location, scale, shape)
      • k

        final double k
        Parameters (location, scale, shape)
    • Constructor Detail

      • GeneralizedExtremeValueDistribution

        public GeneralizedExtremeValueDistribution​(double mu,
                                                   double sigma,
                                                   double k)
        Constructor.
        Parameters:
        mu - Location parameter mu
        sigma - Scale parameter sigma
        k - Shape parameter k
    • Method Detail

      • getMu

        public double getMu()
        Get location.
        Returns:
        Location
      • getSigma

        public double getSigma()
        Get sigma.
        Returns:
        Sigma
      • getK

        public double getK()
        Get the k parameter.
        Returns:
        k
      • pdf

        public double pdf​(double x)
        Description copied from interface: Distribution
        Return the density of an existing value
        Specified by:
        pdf in interface Distribution
        Parameters:
        x - existing value
        Returns:
        distribution density
      • pdf

        public static double pdf​(double x,
                                 double mu,
                                 double sigma,
                                 double k)
        PDF of GEV distribution
        Parameters:
        x - Value
        mu - Location parameter mu
        sigma - Scale parameter sigma
        k - Shape parameter k
        Returns:
        PDF at position x.
      • logpdf

        public double logpdf​(double x)
        Description copied from interface: Distribution
        Return the log density of an existing value
        Specified by:
        logpdf in interface Distribution
        Parameters:
        x - existing value
        Returns:
        log distribution density
      • logpdf

        public static double logpdf​(double x,
                                    double mu,
                                    double sigma,
                                    double k)
        log PDF of GEV distribution
        Parameters:
        x - Value
        mu - Location parameter mu
        sigma - Scale parameter sigma
        k - Shape parameter k
        Returns:
        PDF at position x.
      • cdf

        public double cdf​(double val)
        Description copied from interface: Distribution
        Return the cumulative density function at the given value.
        Specified by:
        cdf in interface Distribution
        Parameters:
        val - existing value
        Returns:
        cumulative density
      • cdf

        public static double cdf​(double val,
                                 double mu,
                                 double sigma,
                                 double k)
        CDF of GEV distribution
        Parameters:
        val - Value
        mu - Location parameter mu
        sigma - Scale parameter sigma
        k - Shape parameter k
        Returns:
        CDF at position x.
      • quantile

        public double quantile​(double val)
        Description copied from interface: Distribution
        Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
        Specified by:
        quantile in interface Distribution
        Parameters:
        val - Quantile to find
        Returns:
        Quantile position
      • quantile

        public static double quantile​(double val,
                                      double mu,
                                      double sigma,
                                      double k)
        Quantile function of GEV distribution
        Parameters:
        val - Value
        mu - Location parameter mu
        sigma - Scale parameter sigma
        k - Shape parameter k
        Returns:
        Quantile function at position x.
      • toString

        public java.lang.String toString()
        Description copied from interface: Distribution
        Describe the distribution
        Specified by:
        toString in interface Distribution
        Overrides:
        toString in class java.lang.Object
        Returns:
        description