BetaSymmetricalBestGen Class Reference

This class implements symmetrical beta random variate generators using Devroye’s one-liner method. More...

Inheritance diagram for BetaSymmetricalBestGen:

Collaboration diagram for BetaSymmetricalBestGen:

Public Member Functions
	BetaSymmetricalBestGen (RandomStream s1, RandomStream s2, RandomStream s3, double alpha)
	Creates a symmetrical beta random variate generator with parameter \(\alpha=\) alpha, using stream s1 to generate \(U_1\), stream s2 to generate \(U_2\) and stream s3 to generate \(S\), as given in equation ( eq.beta.best ).
	BetaSymmetricalBestGen (RandomStream s1, double alpha)
	Creates a symmetrical beta random variate generator with parameter \(\alpha=\) alpha, using only one stream s1 to generate \(U_1\), \(U_2\), and \(S\) as given in equation ( eq.beta.best ).
	BetaSymmetricalBestGen (RandomStream s1, RandomStream s2, RandomStream s3, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using stream s1 to generate \(U_1\), stream s2 to generate \(U_2\) and stream s3 to generate \(S\) as given in equation ( eq.beta.best ).
	BetaSymmetricalBestGen (RandomStream s1, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using only one stream s1.
double	nextDouble ()
RandomStream	getStream2 ()
	Returns stream s2 associated with this object.
RandomStream	getStream3 ()
	Returns stream s3 associated with this object.
Public Member Functions inherited from BetaSymmetricalGen
	BetaSymmetricalGen (RandomStream s, double alpha)
	Creates a new symmetrical beta generator with parameters \(\alpha=\) alpha, over the interval \((0,1)\), using stream s.
	BetaSymmetricalGen (RandomStream s, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using stream s.
Public Member Functions inherited from BetaGen
	BetaGen (RandomStream s, double alpha, double beta, double a, double b)
	Creates a new beta generator with parameters \(\alpha=\) alpha and \(\beta=\) beta, over the interval \((\)a \(,\) b \()\), using stream s.
	BetaGen (RandomStream s, double alpha, double beta)
	Creates a new beta generator with parameters \(\alpha=\) alpha and \(\beta=\) beta, over the interval \((0,1)\), using stream s.
	BetaGen (RandomStream s, BetaDist dist)
	Creates a new generator for the distribution dist, using stream s.
double	getAlpha ()
	Returns the parameter \(\alpha\) of this object.
double	getBeta ()
	Returns the parameter \(\beta\) of this object.
double	getA ()
	Returns the parameter \(a\) of this object.
double	getB ()
	Returns the parameter \(b\) of this object.
Public Member Functions inherited from RandomVariateGen
	RandomVariateGen (RandomStream s, Distribution dist)
	Creates a new random variate generator from the distribution dist, using stream s. More...
double	nextDouble ()
	Generates a random number from the continuous distribution contained in this object. More...
void	nextArrayOfDouble (double[] v, int start, int n)
	Generates n random numbers from the continuous distribution contained in this object. More...
double []	nextArrayOfDouble (int n)
	Generates n random numbers from the continuous distribution contained in this object, and returns them in a new array of size n. More...
RandomStream	getStream ()
	Returns the umontreal.ssj.rng.RandomStream used by this generator. More...
void	setStream (RandomStream stream)
	Sets the umontreal.ssj.rng.RandomStream used by this generator to stream.
Distribution	getDistribution ()
	Returns the umontreal.ssj.probdist.Distribution used by this generator. More...
String	toString ()
	Returns a String containing information about the current generator.

Static Public Member Functions
static double	nextDouble (RandomStream s1, RandomStream s2, RandomStream s3, double alpha)
	Generates a random number using Devroye’s one-liner method. More...
static double	nextDouble (RandomStream s, double alpha)
	Generates a random number using Devroye’s one-liner method with only one stream s. More...
Static Public Member Functions inherited from BetaSymmetricalGen
static double	nextDouble (RandomStream s, double alpha)
Static Public Member Functions inherited from BetaGen
static double	nextDouble (RandomStream s, double alpha, double beta, double a, double b)
	Generates a variate from the beta distribution with parameters \(\alpha= \) alpha, \(\beta= \) beta, over the interval \((a, b)\), using stream s.

Additional Inherited Members
Protected Member Functions inherited from BetaGen
void	setParams (double alpha, double beta, double aa, double bb)
Protected Attributes inherited from BetaGen
double	p
double	q
double	a
double	b
int	gen
Protected Attributes inherited from RandomVariateGen
RandomStream	stream
Distribution	dist

Detailed Description

This class implements symmetrical beta random variate generators using Devroye’s one-liner method.

It is based on Best’s relation [18]  between a Student- \(t\) variate and a symmetrical beta variate:

\[ B_{\alpha, \alpha} \stackrel{\mathcal{L}}{=} \frac{1}{2} \left( 1 + \frac{T_{2\alpha}}{\sqrt{2\alpha+ T_{2\alpha}^2}}\right). \]

If \(S\) is a random sign and \(U_1\), \(U_2\) are two independent uniform \([0,1]\) random variates, then the following gives a symmetrical beta variate [47] :

\[ B_{\alpha, \alpha} \stackrel{\mathcal{L}}{=} \frac{1}{2} + \frac{S}{2 \sqrt{1 + \frac{1}{\left(U_1^{-1/\alpha} - 1\right)\cos^2(2\pi U_2)}}} \tag{eq.beta.best} \]

valid for any shape parameter \(\alpha> 0\).

Member Function Documentation

nextDouble() [1/2]

static double nextDouble ( RandomStream  s1, RandomStream  s2, RandomStream  s3, double  alpha  )

static

Generates a random number using Devroye’s one-liner method.

Restriction: \(\alpha> 0\).

nextDouble() [2/2]

static double nextDouble ( RandomStream  s, double  alpha  )

static

Generates a random number using Devroye’s one-liner method with only one stream s.

Restriction: \(\alpha> 0\).

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The documentation for this class was generated from the following file:

• BetaSymmetricalBestGen.java