SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class GumbelDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.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.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
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
 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.
 String toString()
           
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup
 
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

getMean

public double getMean()
Description copied from class: ContinuousDistribution
Returns the mean.

Specified by:
getMean in interface Distribution
Overrides:
getMean in class ContinuousDistribution
Returns:
the mean

getVariance

public double getVariance()
Description copied from class: ContinuousDistribution
Returns the variance.

Specified by:
getVariance in interface Distribution
Overrides:
getVariance in class ContinuousDistribution
Returns:
the variance

getStandardDeviation

public double getStandardDeviation()
Description copied from class: ContinuousDistribution
Returns the standard deviation.

Specified by:
getStandardDeviation in interface Distribution
Overrides:
getStandardDeviation in class ContinuousDistribution
Returns:
the standard deviation

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 String toString()
Overrides:
toString in class Object

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.