SSJ
V. 2.2.

umontreal.iro.lecuyer.probdist
Class JohnsonSBDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.JohnsonSBDist
All Implemented Interfaces:
Distribution

public class JohnsonSBDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Johnson SB distribution with shape parameters γ and δ > 0, location parameter ξ, and scale parameter λ > 0. Denoting y = (x - ξ)/λ, the density is

f (x) = δ/(λy(1-y)(2π)1/2exp(- (1/2)[γ + δln(y/(1 - y))]2)) for ξ < x < ξ + λ,

and 0 elsewhere. The distribution function is

F(x) = Φ[γ + δln(y/(1 - y))], for ξ < x < ξ + λ,

where Φ is the standard normal distribution function. The inverse distribution function is

F-1(u) = ξ + λ(1/(1 + e-v(u)))        for 0 <= u <= 1,

where

v(u) = [Φ-1(u) - γ]/δ.

This class relies on the methods NormalDist.cdf01 and NormalDist.inverseF01 of NormalDist to approximate Φ and Φ-1.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
JohnsonSBDist(double gamma, double delta, double xi, double lambda)
          Constructs a JohnsonSBDist object with shape parameters γ and δ, location parameter ξ and scale parameter λ.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double gamma, double delta, double xi, double lambda, double x)
          Computes the complementary distribution.
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(double gamma, double delta, double xi, double lambda, double x)
          Computes the distribution function.
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double gamma, double delta, double xi, double lambda, double x)
          Computes the density function.
 double getDelta()
          Returns the value of δ for this object.
 double getGamma()
          Returns the value of γ for this object.
 double getLambda()
          Returns the value of λ for this object.
 double[] getParams()
          Return a table containing the parameters of the current distribution.
 double getXi()
          Returns the value of ξ for this object.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double gamma, double delta, double xi, double lambda, double u)
          Computes the inverse of the distribution.
 void setParams(double gamma, double delta, double xi, double lambda)
          Sets the value of the parameters γ, δ, ξ and λ for this object.
 String toString()
           
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getMean, getStandardDeviation, getVariance, getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

JohnsonSBDist

public JohnsonSBDist(double gamma,
                     double delta,
                     double xi,
                     double lambda)
Constructs a JohnsonSBDist object with shape parameters γ and δ, location parameter ξ and scale parameter λ.

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
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 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

density

public static double density(double gamma,
                             double delta,
                             double xi,
                             double lambda,
                             double x)
Computes the density function.


cdf

public static double cdf(double gamma,
                         double delta,
                         double xi,
                         double lambda,
                         double x)
Computes the distribution function.


barF

public static double barF(double gamma,
                          double delta,
                          double xi,
                          double lambda,
                          double x)
Computes the complementary distribution.


inverseF

public static double inverseF(double gamma,
                              double delta,
                              double xi,
                              double lambda,
                              double u)
Computes the inverse of the distribution.


getGamma

public double getGamma()
Returns the value of γ for this object.


getDelta

public double getDelta()
Returns the value of δ for this object.


getXi

public double getXi()
Returns the value of ξ for this object.


getLambda

public double getLambda()
Returns the value of λ for this object.


setParams

public void setParams(double gamma,
                      double delta,
                      double xi,
                      double lambda)
Sets the value of the parameters γ, δ, ξ and λ for this object.


getParams

public double[] getParams()
Return a table containing the parameters of the current distribution. This table is put in regular order: [γ, δ, ξ, λ].


toString

public String toString()
Overrides:
toString in class Object

SSJ
V. 2.2.

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