BetaSymmetricalBestGen (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.randvar.RandomVariateGen
- - umontreal.iro.lecuyer.randvar.BetaGen
  - - umontreal.iro.lecuyer.randvar.BetaSymmetricalGen
    - - umontreal.iro.lecuyer.randvar.BetaSymmetricalBestGen

```
public class BetaSymmetricalBestGen
extends BetaSymmetricalGen
```
This class implements symmetrical beta random variate generators using Devroye's one-liner method. It is based on Best's relation between a Student-t variate and a symmetrical beta variate:

B_{α, α} $\displaystyle \;\stackrel{{ L}}{{=}}\;$ $\displaystyle {\textstyle\frac{1}{2}}$ (1 + $\displaystyle {\frac{{T_{2\alpha}}}{{\sqrt{2\alpha + T_{2\alpha}^2}}}}$ ).
If S is a random sign and U₁, U₂ are two independent uniform [0, 1] random variates, then the following gives a symmetrical beta variate:

B_{α, α}[tex2html_wrap_indisplay172][tex2html_wrap_indisplay173] + $\displaystyle {\frac{{S}}{{2 \sqrt{1 + \frac{1}{(U_1^{-1/\alpha} - 1)\cos^2(2\pi U_2)}}}}}$
valid for any shape parameter α > 0.

Constructor Summary

Constructors
Constructor and Description
`BetaSymmetricalBestGen(RandomStream s1, BetaSymmetricalDist dist)` Creates a new generator for the distribution `dist`, using only one stream `s1`.
`BetaSymmetricalBestGen(RandomStream s1, double alpha)` Creates a symmetrical beta random variate generator with parameter α = `alpha`, using only one stream `s1` to generate U₁, U₂, and S as given in equation.
`BetaSymmetricalBestGen(RandomStream s1, RandomStream s2, RandomStream s3, BetaSymmetricalDist dist)` Creates a new generator for the distribution `dist`, using stream `s1` to generate U₁, stream `s2` to generate U₂ and stream `s3` to generate S as given in equation.
`BetaSymmetricalBestGen(RandomStream s1, RandomStream s2, RandomStream s3, double alpha)` Creates a symmetrical beta random variate generator with parameter α = `alpha`, using stream `s1` to generate U₁, stream `s2` to generate U₂ and stream `s3` to generate S, as given in equation.

Method Summary

Methods
Modifier and Type	Method and Description
`RandomStream`	`getStream2()` Returns stream `s2` associated with this object.
`RandomStream`	`getStream3()` Returns stream `s3` associated with this object.
`double`	`nextDouble()` Generates a random number from the continuous distribution contained in this object.
`static double`	`nextDouble(RandomStream s, double alpha)` Generates a random number using Devroye's one-liner method with only one stream `s`.
`static double`	`nextDouble(RandomStream s1, RandomStream s2, RandomStream s3, double alpha)` Generates a random number using Devroye's one-liner method.

Methods inherited from class umontreal.iro.lecuyer.randvar.BetaGen
getA, getAlpha, getB, getBeta, nextDouble

Methods inherited from class umontreal.iro.lecuyer.randvar.RandomVariateGen
getDistribution, getStream, nextArrayOfDouble, setStream

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - BetaSymmetricalBestGen
```
public BetaSymmetricalBestGen(RandomStream s1,
                      RandomStream s2,
                      RandomStream s3,
                      double alpha)
```
    Creates a symmetrical beta random variate generator with parameter α = alpha, using stream s1 to generate U₁, stream s2 to generate U₂ and stream s3 to generate S, as given in equation.
  - BetaSymmetricalBestGen
```
public BetaSymmetricalBestGen(RandomStream s1,
                      double alpha)
```
    Creates a symmetrical beta random variate generator with parameter α = alpha, using only one stream s1 to generate U₁, U₂, and S as given in equation.
  - BetaSymmetricalBestGen
```
public BetaSymmetricalBestGen(RandomStream s1,
                      RandomStream s2,
                      RandomStream s3,
                      BetaSymmetricalDist dist)
```
    Creates a new generator for the distribution dist, using stream s1 to generate U₁, stream s2 to generate U₂ and stream s3 to generate S as given in equation.
  - BetaSymmetricalBestGen
```
public BetaSymmetricalBestGen(RandomStream s1,
                      BetaSymmetricalDist dist)
```
    Creates a new generator for the distribution dist, using only one stream s1.
- Method Detail
  - nextDouble
```
public static double nextDouble(RandomStream s1,
                RandomStream s2,
                RandomStream s3,
                double alpha)
```
    Generates a random number using Devroye's one-liner method. Restriction: α > 0.
  - nextDouble
```
public static double nextDouble(RandomStream s,
                double alpha)
```
    Generates a random number using Devroye's one-liner method with only one stream s. Restriction: α > 0.
  - nextDouble
```
public double nextDouble()
```
    Description copied from class: RandomVariateGen
    
    Generates a random number from the continuous distribution contained in this object. By default, this method uses inversion by calling the inverseF method of the distribution object. Alternative generating methods are provided in subclasses.
    
    Overrides:
    
    nextDouble in class RandomVariateGen
    
    Returns:
    the generated value
  - getStream2
```
public RandomStream getStream2()
```
    Returns stream s2 associated with this object.
  - getStream3
```
public RandomStream getStream3()
```
    Returns stream s3 associated with this object.

Class BetaSymmetricalBestGen

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.randvar.BetaGen

Methods inherited from class umontreal.iro.lecuyer.randvar.RandomVariateGen

Methods inherited from class java.lang.Object

Constructor Detail

BetaSymmetricalBestGen

BetaSymmetricalBestGen

BetaSymmetricalBestGen

BetaSymmetricalBestGen

Method Detail

nextDouble

nextDouble

nextDouble

getStream2

getStream3