umontreal.iro.lecuyer.probdist
Class CauchyDist

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

All Implemented Interfaces:

Distribution

public class CauchyDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Cauchy distribution with location parameter α and scale parameter β > 0. The density function is given by

f (x) = β/(π[(x - α)² + β²]) for - ∞ < x < ∞.

The distribution function is

F(x) = 1/2 + arctan((x - α)/β)/π, for - ∞ < x < ∞,

and its inverse is

F^-1(u) = α + βtan(π(u - 1/2)). for 0 < u < 1.

Field Summary

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

decPrec

Constructor Summary

CauchyDist()
Constructs a CauchyDist object with parameters α = 0 and β = 1.

CauchyDist(double alpha, double beta)
Constructs a CauchyDist object with parameters α = alpha and β = beta.

Method Summary

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
static double	barF(double alpha, double beta, double x) Computes the complementary distribution.
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(double alpha, double beta, 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 beta, double x) Computes the density function.
double	getAlpha() Returns the value of α for this object.
double	getBeta() Returns the value of β for this object.
double	inverseF(double u) Computes and returns the inverse distribution function F-1(u), defined in.
static double	inverseF(double alpha, double beta, double u) Computes the inverse of the distribution.
void	setParams(double alpha, double beta) Sets the value of the parameters α and β for 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

CauchyDist

public CauchyDist()

Constructs a CauchyDist object with parameters α = 0 and β = 1.

CauchyDist

public CauchyDist(double alpha,
                  double beta)

Constructs a CauchyDist object with parameters α = alpha and β = beta.

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 beta,
                             double x)

Computes the density function.

cdf

public static double cdf(double alpha,
                         double beta,
                         double x)

Computes the distribution function.

barF

public static double barF(double alpha,
                          double beta,
                          double x)

Computes the complementary distribution.

inverseF

public static double inverseF(double alpha,
                              double beta,
                              double u)

Computes the inverse of the distribution.

getAlpha

public double getAlpha()

Returns the value of α for this object.

getBeta

public double getBeta()

Returns the value of β for this object.

setParams

public void setParams(double alpha,
                      double beta)

Sets the value of the parameters α and β for this object.