Documentation of 'umontreal.iro.lecuyer.probdist.GumbelDist' Java class
GumbelDist
Skip navigation links
umontreal.iro.lecuyer.probdist

Class GumbelDist

  • All Implemented Interfaces:
    Distribution

    public class GumbelDist
extends ContinuousDistribution
    Extends the class ContinuousDistribution for the Gumbel distribution, with location parameter δ and scale parameter β≠ 0. Using the notation z = (x - δ)/β, it has density

    f (x) = e-ze-e-z/| β|,        for - ∞ < x < ∞.

    and distribution function

    F(x) = e-e-z,        for β > 0

    F(x) = 1 - e-e-z,        for β < 0.

    • Constructor Summary

      Constructors 
      Constructor and Description
      GumbelDist()
      Constructor for the standard Gumbel distribution with parameters β = 1 and δ = 0.
      GumbelDist(double beta, double delta)
      Constructs a GumbelDist object with parameters β = beta and δ = delta.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double barF(double x)
      Returns the complementary distribution function.
      static double barF(double beta, double delta, double x)
      Computes and returns the complementary distribution function 1 - F(x).
      double cdf(double x)
      Returns the distribution function F(x).
      static double cdf(double beta, double delta, double x)
      Computes and returns the distribution function.
      double density(double x)
      Returns f (x), the density evaluated at x.
      static double density(double beta, double delta, double x)
      Computes and returns the density function.
      double getBeta()
      Returns the parameter β of this object.
      double getDelta()
      Returns the parameter δ of this object.
      static GumbelDist getInstanceFromMLE(double[] x, int n)
      Creates a new instance of an Gumbel distribution with parameters β and δ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1, assuming that β > 0.
      static GumbelDist getInstanceFromMLEmin(double[] x, int n)
      Similar to getInstanceFromMLE, but for the case β < 0.
      double getMean()
      Returns the mean.
      static double getMean(double beta, double delta)
      Returns the mean, E[X] = δ + γβ, of the Gumbel distribution with parameters β and δ, where γ = 0.5772156649015329 is the Euler-Mascheroni constant.
      static double[] getMLE(double[] x, int n)
      Estimates the parameters (β, δ) of the Gumbel distribution, assuming that β > 0, and using the maximum likelihood method with the n observations x[i], i = 0, 1,…, n - 1.
      static double[] getMLEmin(double[] x, int n)
      Similar to getMLE, but for the case β < 0.
      double[] getParams()
      Return a table containing the parameters of the current distribution.
      double getStandardDeviation()
      Returns the standard deviation.
      static double getStandardDeviation(double beta, double delta)
      Returns the standard deviation of the Gumbel distribution with parameters β and δ.
      double getVariance()
      Returns the variance.
      static double getVariance(double beta, double delta)
      Returns the variance Var[X] = π2β2/6 of the Gumbel distribution with parameters β and δ.
      double inverseF(double u)
      Returns the inverse distribution function x = F-1(u).
      static double inverseF(double beta, double delta, double u)
      Computes and returns the inverse distribution function.
      void setParams(double beta, double delta)
      Sets the parameters β and δ of this object.
      java.lang.String toString() 

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

    • Constructor Detail

      • GumbelDist

        public GumbelDist()
        Constructor for the standard Gumbel distribution with parameters β = 1 and δ = 0.

      • GumbelDist

        public GumbelDist(double beta,
                  double delta)
        Constructs a GumbelDist object with parameters β = beta and δ = delta.

    • Method Detail

      • density

        public double density(double x)
        Description copied from class: ContinuousDistribution
        Returns f (x), the density evaluated at x.
        Specified by:
        density in class ContinuousDistribution
        Parameters:
        x - value at which the density is evaluated
        Returns:
        density function evaluated at x

      • cdf

        public double cdf(double x)
        Description copied from interface: Distribution
        Returns the distribution function F(x).
        Parameters:
        x - value at which the distribution function is evaluated
        Returns:
        distribution function evaluated at x

      • barF

        public double barF(double x)
        Description copied from class: ContinuousDistribution
        Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
        Specified by:
        barF in interface Distribution
        Overrides:
        barF in class ContinuousDistribution
        Parameters:
        x - value at which the complementary distribution function is evaluated
        Returns:
        complementary distribution function evaluated at x

      • inverseF

        public double inverseF(double u)
        Description copied from class: ContinuousDistribution
        Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].
        Specified by:
        inverseF in interface Distribution
        Overrides:
        inverseF in class ContinuousDistribution
        Parameters:
        u - value at which the inverse distribution function is evaluated
        Returns:
        the inverse distribution function evaluated at u

      • density

        public static double density(double beta,
                             double delta,
                             double x)
        Computes and returns the density function.

      • cdf

        public static double cdf(double beta,
                         double delta,
                         double x)
        Computes and returns the distribution function.

      • barF

        public static double barF(double beta,
                          double delta,
                          double x)
        Computes and returns the complementary distribution function 1 - F(x).

      • inverseF

        public static double inverseF(double beta,
                              double delta,
                              double u)
        Computes and returns the inverse distribution function.

      • getMLE

        public static double[] getMLE(double[] x,
                              int n)
        Estimates the parameters (β, δ) of the Gumbel distribution, assuming that β > 0, and using the maximum likelihood method with the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [β, δ].
        Parameters:
        x - the list of observations used to evaluate parameters
        n - the number of observations used to evaluate parameters
        Returns:
        returns the parameters [ hat(δ), hat(β)]

      • getMLEmin

        public static double[] getMLEmin(double[] x,
                                 int n)
        Similar to getMLE, but for the case β < 0.
        Parameters:
        x - the list of observations used to evaluate parameters
        n - the number of observations used to evaluate parameters
        Returns:
        returns the parameters [ hat(δ), hat(β)]

      • getInstanceFromMLE

        public static GumbelDist getInstanceFromMLE(double[] x,
                                            int n)
        Creates a new instance of an Gumbel distribution with parameters β and δ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1, assuming that β > 0.
        Parameters:
        x - the list of observations to use to evaluate parameters
        n - the number of observations to use to evaluate parameters

      • getInstanceFromMLEmin

        public static GumbelDist getInstanceFromMLEmin(double[] x,
                                               int n)
        Similar to getInstanceFromMLE, but for the case β < 0.
        Parameters:
        x - the list of observations to use to evaluate parameters
        n - the number of observations to use to evaluate parameters

      • getMean

        public static double getMean(double beta,
                             double delta)
        Returns the mean, E[X] = δ + γβ, of the Gumbel distribution with parameters β and δ, where γ = 0.5772156649015329 is the Euler-Mascheroni constant.
        Returns:
        the mean of the Extreme Value distribution E[X] = δ + γ*β

      • getVariance

        public static double getVariance(double beta,
                                 double delta)
        Returns the variance Var[X] = π2β2/6 of the Gumbel distribution with parameters β and δ.
        Returns:
        the variance of the Gumbel distribution Var[X] = ()πβ)2/6

      • getStandardDeviation

        public static double getStandardDeviation(double beta,
                                          double delta)
        Returns the standard deviation of the Gumbel distribution with parameters β and δ.
        Returns:
        the standard deviation of the Gumbel distribution

      • getBeta

        public double getBeta()
        Returns the parameter β of this object.

      • getDelta

        public double getDelta()
        Returns the parameter δ of this object.

      • setParams

        public void setParams(double beta,
                      double delta)
        Sets the parameters β and δ of this object.

      • getParams

        public double[] getParams()
        Return a table containing the parameters of the current distribution. This table is put in regular order: [β, δ].

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object
Skip navigation links

DMelt 3.0 © DataMelt by jWork.ORG

You see the box below because you did not login.