umontreal.iro.lecuyer.probdist
Class ParetoDist

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

All Implemented Interfaces:

Distribution

public class ParetoDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for a distribution from the Pareto family, with shape parameter α > 0 and location parameter β > 0. The density for this type of Pareto distribution is

f (x) = αβ^αx^-(α-1) for x >= β,

and 0 otherwise. The distribution function is

F(x) = 1 - (β/x)^α for x >= β,

and the inverse distribution function is

F^-1(u) = β(1 - u)^-1/α for 0 <= u < 1.

Field Summary

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

decPrec

Constructor Summary

ParetoDist(double alpha)
Constructs a ParetoDist object with parameters α = alpha and β = 1.

ParetoDist(double alpha, double beta)
Constructs a ParetoDist 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 function.
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 parameter α.
double	getBeta() Returns the parameter β.
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 function.
void	setParams(double alpha, double beta) Sets the parameter 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

ParetoDist

public ParetoDist(double alpha)

Constructs a ParetoDist object with parameters α = alpha and β = 1.

ParetoDist

public ParetoDist(double alpha,
                  double beta)

Constructs a ParetoDist 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 function.

inverseF

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

Computes the inverse of the distribution function.

getAlpha

public double getAlpha()

Returns the parameter α.

getBeta

public double getBeta()

Returns the parameter β.

setParams

public void setParams(double alpha,
                      double beta)

Sets the parameter α and β for this object.