umontreal.iro.lecuyer.probdist
Class LaplaceDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      umontreal.iro.lecuyer.probdist.LaplaceDist

All Implemented Interfaces:

Distribution

public class LaplaceDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Laplace distribution. It has location parameter θ and scale parameter φ > 0. The density function is given by

f (x) = e^{-| x-θ|/φ}/(2φ) for - ∞ < x < ∞.

The distribution function is

F(x) =	(1/2)e(x-θ)/φ	if x <= θ,
F(x) =	1 - (1/2)e(θ-x)/φ	otherwise,

and its inverse is

F-1(u) =	φlog(2u) + θ	if 0 <= u <= 1/2,
F-1(u) =	θ - φlog(2(1 - u))	otherwise.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

LaplaceDist()
Constructs a LaplaceDist object with default parameters θ = 0 and φ = 1.

LaplaceDist(double theta, double phi)
Constructs a LaplaceDist object with parameters θ = theta and φ = phi.

Method Summary

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
static double	barF(double theta, double phi, double x) Computes the Laplace complementary distribution function.
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(double theta, double phi, double x) Computes the Laplace distribution function.
double	density(double x) Returns f (x), the density of X evaluated at x.
static double	density(double theta, double phi, double x) Computes the Laplace density function.
double	getPhi() Returns the parameter φ.
double	getTheta() Returns the parameter θ.
double	inverseF(double u) Computes and returns the inverse distribution function F-1(u), defined in.
static double	inverseF(double theta, double phi, double u) Computes the inverse Laplace distribution function.

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

LaplaceDist

public LaplaceDist()

Constructs a LaplaceDist object with default parameters θ = 0 and φ = 1.

LaplaceDist

public LaplaceDist(double theta,
                   double phi)

Constructs a LaplaceDist object with parameters θ = theta and φ = phi.

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 theta,
                             double phi,
                             double x)

Computes the Laplace density function.

cdf

public static double cdf(double theta,
                         double phi,
                         double x)

Computes the Laplace distribution function.

barF

public static double barF(double theta,
                          double phi,
                          double x)

Computes the Laplace complementary distribution function.

inverseF

public static double inverseF(double theta,
                              double phi,
                              double u)

Computes the inverse Laplace distribution function.

getTheta

public double getTheta()

Returns the parameter θ.

getPhi

public double getPhi()

Returns the parameter φ.