SSJ
V. labo.

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

GumbelDist

Extends the class ContinuousDistribution for the Gumbel distribution[#!tJOH95b!#, page 2], 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 < ∞.$\displaystyle \eqlabel$eq:densgumbel

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()
          .
GumbelDist(double beta, double delta)
          .
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double beta, double delta, double x)
          .
 double cdf(double x)
          .
static double cdf(double beta, double delta, double x)
          .
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double beta, double delta, double x)
          .
 double getBeta()
          .
 double getDelta()
          .
static GumbelDist getInstanceFromMLE(double[] x, int n)
          .
static GumbelDist getInstanceFromMLEmin(double[] x, int n)
          .
 double getMean()
          Returns the mean.
static double getMean(double beta, double delta)
          .
static double[] getMLE(double[] x, int n)
          .
static double[] getMLEmin(double[] x, int n)
          .
 double[] getParams()
          .
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double beta, double delta)
          .
 double getVariance()
          Returns the variance.
static double getVariance(double beta, double delta)
          .
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double beta, double delta, double u)
          .
 void setParams(double beta, double delta)
          .
 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()
. \begin{tabb}Constructor for the standard
 Gumbel distribution with parameters $\beta$\ = 1 and $\delta$\ = 0.
 \end{tabb}


GumbelDist

public GumbelDist(double beta,
                  double delta)
. \begin{tabb}Constructs a \texttt{GumbelDist} object with parameters
 $\beta$\ = \texttt{beta} and $\delta$\ = \texttt{delta}.
 \end{tabb}

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
. \begin{tabb}Returns the distribution function $F(x)$.
 \end{tabb}
xvalue at which the distribution function is evaluated 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)
. \begin{tabb}Computes and returns the density function.
 \end{tabb}


cdf

public static double cdf(double beta,
                         double delta,
                         double x)
. \begin{tabb}
 Computes and returns the distribution function.
 \end{tabb}


barF

public static double barF(double beta,
                          double delta,
                          double x)
. \begin{tabb}
 Computes and returns the complementary distribution function $1 - F(x)$.
 \end{tabb}


inverseF

public static double inverseF(double beta,
                              double delta,
                              double u)
. \begin{tabb}
 Computes and returns the inverse distribution function.
 \end{tabb}


getMLE

public static double[] getMLE(double[] x,
                              int n)
. \begin{tabb}
 Estimates the parameters $(\beta,\delta)$\ of the Gumbel distribut...
 ...ere $\bar x_n$\ is the average of $x[0],\dots,x[n-1]$.
 \end{detailed}\end{tabb}
xthe list of observations used to evaluate parameters nthe number of observations used to evaluate parameters returns the parameters [ $ \hat{{\delta}}$, $ \hat{{\beta}}$]


getMLEmin

public static double[] getMLEmin(double[] x,
                                 int n)
. \begin{tabb}
 Similar to \method{getMLE}{}, but \emph{for the case $\beta < 0$}.
 \end{tabb}
xthe list of observations used to evaluate parameters nthe number of observations used to evaluate parameters returns the parameters [ [tex2html_wrap_inline322], [tex2html_wrap_inline324]]


getInstanceFromMLE

public static GumbelDist getInstanceFromMLE(double[] x,
                                            int n)
. \begin{tabb}
 Creates a new instance of an Gumbel distribution with parameters
 ...
 ...ns $x[i]$, $i = 0, 1, \ldots, n-1$, \emph{assuming that $\beta > 0$}.
 \end{tabb}
xthe list of observations to use to evaluate parameters nthe number of observations to use to evaluate parameters


getInstanceFromMLEmin

public static GumbelDist getInstanceFromMLEmin(double[] x,
                                               int n)
. \begin{tabb}
 Similar to \method{getInstanceFromMLE}{}, but \emph{for the case $\beta < 0$}.
 \end{tabb}
xthe list of observations to use to evaluate parameters nthe number of observations to use to evaluate parameters


getMean

public static double getMean(double beta,
                             double delta)
. \begin{tabb}Returns the mean, $E[X] = \delta + \gamma\beta$,
 of the Gumbel dist...
 ...here $\gamma = 0.5772156649015329$\ is the Euler-Mascheroni constant.
 \end{tabb}
the mean of the Extreme Value distribution E[X] = δ + γ*β


getVariance

public static double getVariance(double beta,
                                 double delta)
. \begin{tabb}Returns the variance $\mbox{Var}[X] =
 \pi^2 \beta^2\!/6$\ of the Gumbel distribution with parameters $\beta$\ and $\delta$.
 \end{tabb}
the variance of the Gumbel distribution Var[X] = ()πβ)2/6


getStandardDeviation

public static double getStandardDeviation(double beta,
                                          double delta)
. \begin{tabb}Returns the standard deviation
 of the Gumbel distribution with parameters $\beta$\ and $\delta$.
 \end{tabb}
the standard deviation of the Gumbel distribution


getBeta

public double getBeta()
. \begin{tabb}Returns the parameter $\beta$\ of this object.
 \end{tabb}


getDelta

public double getDelta()
. \begin{tabb}
 Returns the parameter $\delta$\ of this object.
 \end{tabb}


setParams

public void setParams(double beta,
                      double delta)
. \begin{tabb}
 Sets the parameters $\beta$\ and $\delta$\ of this object.
 \end{tabb}


getParams

public double[] getParams()
. \begin{tabb}
 Return a table containing the parameters of the current distribution.
 This table is put in regular order: [$\beta$, $\delta$].
 \end{tabb}

 


toString

public String toString()
. \begin{hide}
 \par
 \begin{tabb}
 Returns a \texttt{String} containing information about the current distribution.
 \end{tabb}\end{hide}

Overrides:
toString in class Object

SSJ
V. labo.

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