BetaSymmetricalPolarGen Class Reference

This class implements symmetrical beta random variate generators using Ulrich’s polar method [232] . More...

Inheritance diagram for BetaSymmetricalPolarGen:

Collaboration diagram for BetaSymmetricalPolarGen:

Public Member Functions
	BetaSymmetricalPolarGen (RandomStream s1, RandomStream s2, double alpha)
	Creates a symmetrical beta random variate generator with parameter \(\alpha=\) alpha, using stream s1 to generate \(x\) and stream s2 to generate \(y\), as in ( eq.beta.ulrich ) above. More...
	BetaSymmetricalPolarGen (RandomStream s1, double alpha)
	Creates a symmetrical beta random variate generator with parameter \(\alpha=\) alpha, using stream s1 to generate \(x\) and \(y\), as in ( eq.beta.ulrich ) above. More...
	BetaSymmetricalPolarGen (RandomStream s1, RandomStream s2, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using stream s1 to generate \(x\) and stream s2 to generate \(y\), as in ( eq.beta.ulrich ) above. More...
	BetaSymmetricalPolarGen (RandomStream s1, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using only one stream s1. More...
double	nextDouble ()
RandomStream	getStream2 ()
	Returns stream s2 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, double alpha)
	Generates a random number using Ulrich’s polar method. More...
static double	nextDouble (RandomStream s, double alpha)
	Generates a random number by Ulrich’s polar method using 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 Ulrich’s polar method [232] .

The method generates two uniform random variables \(x \in[0, 1]\) and \(y \in[-1, 1]\) until \(x^2 + y^2 \le1\). Then it returns

\[ \frac{1}{2} + \frac{xy}{S}\sqrt{1 - S^{2/(2\alpha- 1)}} \tag{eq.beta.ulrich} \]

where \(S = x^2 + y^2\), and \(\alpha\) is the shape parameter of the beta distribution. The method is valid only when \(\alpha> 1/2\).

Constructor & Destructor Documentation

BetaSymmetricalPolarGen() [1/4]

BetaSymmetricalPolarGen	(	RandomStream	s1,
		RandomStream	s2,
		double	alpha
	)

Creates a symmetrical beta random variate generator with parameter \(\alpha=\) alpha, using stream s1 to generate \(x\) and stream s2 to generate \(y\), as in ( eq.beta.ulrich ) above.

Restriction: \(\alpha> 1/2\).

BetaSymmetricalPolarGen() [2/4]

BetaSymmetricalPolarGen	(	RandomStream	s1,
		double	alpha
	)

Creates a symmetrical beta random variate generator with parameter \(\alpha=\) alpha, using stream s1 to generate \(x\) and \(y\), as in ( eq.beta.ulrich ) above.

Restriction: \(\alpha> 1/2\).

BetaSymmetricalPolarGen() [3/4]

BetaSymmetricalPolarGen	(	RandomStream	s1,
		RandomStream	s2,
		BetaSymmetricalDist	dist
	)

Creates a new generator for the distribution dist, using stream s1 to generate \(x\) and stream s2 to generate \(y\), as in ( eq.beta.ulrich ) above.

Restriction: dist must have \(\alpha> 1/2\).

BetaSymmetricalPolarGen() [4/4]

BetaSymmetricalPolarGen	(	RandomStream	s1,
		BetaSymmetricalDist	dist
	)

Creates a new generator for the distribution dist, using only one stream s1.

Restriction: dist must have \(\alpha> 1/2\).

Member Function Documentation

nextDouble() [1/2]

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

static

Generates a random number using Ulrich’s polar method.

Stream s1 generates \(x\) and stream s2 generates \(y\) [see eq. ( eq.beta.ulrich )]. Restriction: \(\alpha> 1/2\).

nextDouble() [2/2]

static double nextDouble ( RandomStream  s, double  alpha  )

static

Generates a random number by Ulrich’s polar method using stream s.

Restriction: \(\alpha> 1/2\).

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

• BetaSymmetricalPolarGen.java