JohnsonSUDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.JohnsonSUDist

All Implemented Interfaces:

Distribution
```
public class JohnsonSUDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the Johnson S_U 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(e^t(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

Constructors
Constructor and Description
`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

Methods
Modifier and Type	Method and Description
`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 function 1 - F(x).
`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 F(x).
`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 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.
`static double`	`getMean(double gamma, double delta, double xi, double lambda)` Computes and returns the mean of the Johnson S_U distribution with parameters γ, δ, ξ and λ.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(double gamma, double delta, double xi, double lambda)` Computes and returns the standard deviation of the Johnson S_U distribution with parameters γ, δ, ξ and λ.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(double gamma, double delta, double xi, double lambda)` Computes and returns the variance of the Johnson S_U distribution with parameters γ, δ, ξ and λ.
`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 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.
`java.lang.String`	`toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, 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 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
  - getMean
```
public double getMean()
```
    Description copied from class: ContinuousDistribution
    
    Returns the mean.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class ContinuousDistribution
    
    Returns:
    the mean
  - getVariance
```
public double getVariance()
```
    Description copied from class: ContinuousDistribution
    
    Returns the variance.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    the variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: ContinuousDistribution
    
    Returns the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class ContinuousDistribution
    
    Returns:
    the standard deviation
  - 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 S_U distribution with parameters γ, δ, ξ and λ.
    
    Returns:
    the mean of the Johnson S_U distribution E[X] = ξ - λexp^1/(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 S_U distribution with parameters γ, δ, ξ and λ.
    
    Returns:
    the variance of the Johnson S_U distribution Var[X] = (λ²/2)(exp^1/δ² -1)(exp^1/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 S_U distribution with parameters γ, δ, ξ and λ.
    
    Returns:
    the standard deviation of the Johnson S_U 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 java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class JohnsonSUDist

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

JohnsonSUDist

JohnsonSUDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getGamma

getDelta

getXi

getLambda

setParams

getParams

toString