umontreal.iro.lecuyer.probdist
Class ExtremeValueDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      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.
double	getLambda() Returns the parameter λ of this object.
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

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.

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.