SSJ
V. 1.2.5.

umontreal.iro.lecuyer.probdist
Class ExtremeValueDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.ExtremeValueDist
All Implemented Interfaces:
Distribution

public class ExtremeValueDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the extreme value (or Gumbel) distribution, with location parameter α and scale parameter λ > 0. It has density

f (x) = λe-λ(x-α)e-e-λ(x-α),                for - ∞ < x < ∞.

distribution function

F(x) = e-e-λ(x-α)                for - ∞ < x < ∞,

and inverse distribution function

F-1(u) = - ln(- ln(u))/λ + α,        for 0 <= u <= 1.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
ExtremeValueDist()
          Constructs a ExtremeValueDist object with parameters α = 0 and λ = 1.
ExtremeValueDist(double alpha, double lambda)
          Constructs a ExtremeValueDist object with parameters α = alpha and λ = lambda.
 
Method Summary
 double barF(double x)
          Returns bar(F)(x) = 1 - F(x).
static double barF(double alpha, double lambda, double x)
          Computes the complementary distribution function.
 double cdf(double x)
          Computes and returns the distribution function F(x).
static double cdf(double alpha, double lambda, double x)
          Computes the distribution function.
 double density(double x)
          Returns f (x), the density of X evaluated at x.
static double density(double alpha, double lambda, double x)
          Computes the density function.
 double getAlpha()
          Returns the parameter α of this object.
static ExtremeValueDist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of an extreme value distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
 double getLambda()
          Returns the parameter λ of this object.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Estimates and returns the parameters [ hat(α), hat(λ)] of the extreme value distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
 double getMean()
          Returns the mean of the distribution function.
static double getMean(double alpha, double lambda)
          Computes and returns the mean, E[X] = α + γ/λ, of the extreme value distribution with parameters α and λ, where γ = 0.5772156649 is the Euler-Mascheroni constant.
 double getStandardDeviation()
          Returns the standard deviation of the distribution function.
static double getStandardDeviation(double alpha, double lambda)
          Computes and returns the standard deviation of the extreme value distribution with parameters α and λ.
 double getVariance()
          Returns the variance of the distribution function.
static double getVariance(double alpha, double lambda)
          Computes and returns the variance, Var[X] = π2/(6λ2), of the extreme value distribution with parameters α and λ.
 double inverseF(double u)
          Computes and returns the inverse distribution function F-1(u), defined in.
static double inverseF(double alpha, double lambda, double u)
          Computes the inverse distribution function.
 void setParams(double alpha, double lambda)
          Sets the parameters α and λ of this object.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

ExtremeValueDist

public ExtremeValueDist()
Constructs a ExtremeValueDist object with parameters α = 0 and λ = 1.


ExtremeValueDist

public ExtremeValueDist(double alpha,
                        double lambda)
Constructs a ExtremeValueDist object with parameters α = alpha and λ = lambda.

Method Detail

density

public double density(double x)
Description copied from class: ContinuousDistribution
Returns f (x), the density of X 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
Computes and 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 interface: Distribution
Returns 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 interface: Distribution
Computes and returns the inverse distribution function F-1(u), defined in.

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value in the interval (0, 1) for which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


density

public static double density(double alpha,
                             double lambda,
                             double x)
Computes the density function.


cdf

public static double cdf(double alpha,
                         double lambda,
                         double x)
Computes the distribution function.


barF

public static double barF(double alpha,
                          double lambda,
                          double x)
Computes the complementary distribution function.


inverseF

public static double inverseF(double alpha,
                              double lambda,
                              double u)
Computes the inverse distribution function.


getInstanceFromMLE

public static ExtremeValueDist getInstanceFromMLE(double[] x,
                                                  int n)
Creates a new instance of an extreme value distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameters

getMaximumLikelihoodEstimate

public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                    int n)
Estimates and returns the parameters [ hat(α), hat(λ)] of the extreme value distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.

Parameters:
x - the list of observations used to evaluate parameters
n - the number of observations used to evaluate parameters
Returns:
returns the parameters [ hat(α), hat(λ)]

getMean

public static double getMean(double alpha,
                             double lambda)
Computes and returns the mean, E[X] = α + γ/λ, of the extreme value distribution with parameters α and λ, where γ = 0.5772156649 is the Euler-Mascheroni constant.

Returns:
the mean of the Extreme Value distribution E[X] = α + γ/λ

getVariance

public static double getVariance(double alpha,
                                 double lambda)
Computes and returns the variance, Var[X] = π2/(6λ2), of the extreme value distribution with parameters α and λ.

Returns:
the variance of the extreme value distribution Var[X] = 1/6π21/λ2

getStandardDeviation

public static double getStandardDeviation(double alpha,
                                          double lambda)
Computes and returns the standard deviation of the extreme value distribution with parameters α and λ.

Returns:
the standard deviation of the extreme value distribution

getAlpha

public double getAlpha()
Returns the parameter α of this object.


getLambda

public double getLambda()
Returns the parameter λ of this object.


setParams

public void setParams(double alpha,
                      double lambda)
Sets the parameters α and λ of this object.


SSJ
V. 1.2.5.

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