SSJ
V. 1.2.5.

umontreal.iro.lecuyer.probdist
Class JohnsonSUDist

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

public class JohnsonSUDist
extends ContinuousDistribution

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

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

and distribution function

F(x) = Φ{γ + δln[y + (y^2 + 1)1/2]},        for - ∞ < x < ∞,

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

F-1(u) = ξ + λ(et(u) - e-t(u))/2,        for 0 <= u < 1,

where

t(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
JohnsonSUDist(double gamma, double delta)
          Same as JohnsonSUDist (gamma, delta, 0.0, 1.0).
JohnsonSUDist(double gamma, double delta, double xi, double lambda)
          Constructs a JohnsonSUDist object with shape parameters γ and δ, location parameter ξ, and scale parameter λ.
 
Method Summary
static double barF(double gamma, double delta, double xi, double lambda, double x)
          Computes the complementary distribution function 1 - F(x).
 double cdf(double x)
          Computes and returns the distribution function F(x).
static double cdf(double gamma, double delta, double xi, double lambda, double x)
          Computes the distribution function F(x).
 double density(double x)
          Returns f (x), the density of X evaluated at x.
static double density(double gamma, double delta, double xi, double lambda, double x)
          Computes the density function f (x).
 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 getMean()
          Returns the mean of the distribution function.
static double getMean(double gamma, double delta, double xi, double lambda)
          Computes and returns the mean of the Johnson SU distribution with parameters γ, δ, ξ and λ.
 double getStandardDeviation()
          Returns the standard deviation of the distribution function.
static double getStandardDeviation(double gamma, double delta, double xi, double lambda)
          Computes and returns the standard deviation of the Johnson SU distribution with parameters γ, δ, ξ and λ.
 double getVariance()
          Returns the variance of the distribution function.
static double getVariance(double gamma, double delta, double xi, double lambda)
          Computes and returns the variance of the Johnson SU distribution with parameters γ, δ, ξ and λ.
 double getXi()
          Returns the value of ξ for this object.
 double inverseF(double u)
          Computes and returns the inverse distribution function F-1(u), defined in.
static double inverseF(double gamma, double delta, double xi, double lambda, double u)
          Computes the inverse distribution function F-1(u).
 void setParams(double gamma, double delta, double xi, double lambda)
          Sets the value of the parameters γ, δ, ξ and λ for this object.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
barF, inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

JohnsonSUDist

public JohnsonSUDist(double gamma,
                     double delta)
Same as JohnsonSUDist (gamma, delta, 0.0, 1.0).


JohnsonSUDist

public JohnsonSUDist(double gamma,
                     double delta,
                     double xi,
                     double lambda)
Constructs a JohnsonSUDist 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 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

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

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


density

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


cdf

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


barF

public static double barF(double gamma,
                          double delta,
                          double xi,
                          double lambda,
                          double x)
Computes the complementary distribution function 1 - F(x).


inverseF

public static double inverseF(double gamma,
                              double delta,
                              double xi,
                              double lambda,
                              double u)
Computes the inverse distribution function F-1(u).


getMean

public static double getMean(double gamma,
                             double delta,
                             double xi,
                             double lambda)
Computes and returns the mean of the Johnson SU distribution with parameters γ, δ, ξ and λ.

Returns:
the mean of the Johnson SU distribution E[X] = ξ - λexp1/(2δ2)sinh(γ/δ)

getVariance

public static double getVariance(double gamma,
                                 double delta,
                                 double xi,
                                 double lambda)
Computes and returns the variance of the Johnson SU distribution with parameters γ, δ, ξ and λ.

Returns:
the variance of the Johnson SU distribution Var[X] = (λ2/2)(exp1/δ2 -1)(exp1/δ2cosh(2γ/δ) + 1)

getStandardDeviation

public static double getStandardDeviation(double gamma,
                                          double delta,
                                          double xi,
                                          double lambda)
Computes and returns the standard deviation of the Johnson SU distribution with parameters γ, δ, ξ and λ.

Returns:
the standard deviation of the Johnson SU 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.


SSJ
V. 1.2.5.

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