This class implements symmetrical beta random variate generators using Ulrich’s polar method [223] . More...

Inheritance diagram for umontreal.ssj.randvar.BetaSymmetricalPolarGen:

Public Member Functions
	BetaSymmetricalPolarGen (RandomStream s1, RandomStream s2, double alpha)
	Creates a symmetrical beta random variate generator with parameter.
	BetaSymmetricalPolarGen (RandomStream s1, double alpha)
	Creates a symmetrical beta random variate generator with parameter.
	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.
	BetaSymmetricalPolarGen (RandomStream s1, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using only one stream s1.
double	nextDouble ()
	Generates a random number from the continuous distribution contained in this object.
RandomStream	getStream2 ()
	Returns stream s2 associated with this object.
Public Member Functions inherited from umontreal.ssj.randvar.BetaSymmetricalGen
	BetaSymmetricalGen (RandomStream s, double alpha)
	Creates a new symmetrical beta generator with parameters.
	BetaSymmetricalGen (RandomStream s, BetaSymmetricalDist dist)
	Creates a new generator for the distribution dist, using stream s.
Public Member Functions inherited from umontreal.ssj.randvar.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.
	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 umontreal.ssj.randvar.RandomVariateGen
	RandomVariateGen (RandomStream s, Distribution dist)
	Creates a new random variate generator from the distribution dist, using stream s.
void	nextArrayOfDouble (double[] v, int start, int n)
	Generates n random numbers from the continuous distribution contained in this object.
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.
RandomStream	getStream ()
	Returns the umontreal.ssj.rng.RandomStream used by this generator.
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.
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.
static double	nextDouble (RandomStream s, double alpha)
	Generates a random number by Ulrich’s polar method using stream s.
Static Public Member Functions inherited from umontreal.ssj.randvar.BetaGen
static double	nextDouble (RandomStream s, double alpha, double beta, double a, double b)
	Generates a variate from the beta distribution with parameters.

Detailed Description

This class implements symmetrical beta random variate generators using Ulrich’s polar method [223] .

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 \(\alpha> 1/2\).

Definition at line 47 of file BetaSymmetricalPolarGen.java.

Constructor & Destructor Documentation

◆ BetaSymmetricalPolarGen() [1/4]

umontreal.ssj.randvar.BetaSymmetricalPolarGen.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: \(\alpha> 1/2\).

Definition at line 59 of file BetaSymmetricalPolarGen.java.

◆ BetaSymmetricalPolarGen() [2/4]

umontreal.ssj.randvar.BetaSymmetricalPolarGen.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: \(\alpha> 1/2\).

Definition at line 75 of file BetaSymmetricalPolarGen.java.

◆ BetaSymmetricalPolarGen() [3/4]

umontreal.ssj.randvar.BetaSymmetricalPolarGen.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 \(\alpha> 1/2\).

Definition at line 85 of file BetaSymmetricalPolarGen.java.

◆ BetaSymmetricalPolarGen() [4/4]

umontreal.ssj.randvar.BetaSymmetricalPolarGen.BetaSymmetricalPolarGen	(	RandomStream	s1,
		BetaSymmetricalDist	dist )

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

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

Definition at line 99 of file BetaSymmetricalPolarGen.java.

Member Function Documentation

◆ getStream2()

RandomStream umontreal.ssj.randvar.BetaSymmetricalPolarGen.getStream2 ( )

Returns stream s2 associated with this object.

Definition at line 141 of file BetaSymmetricalPolarGen.java.

◆ nextDouble() [1/3]

double umontreal.ssj.randvar.BetaSymmetricalPolarGen.nextDouble ( )

Generates a random number from the continuous distribution contained in this object.

By default, this method uses inversion by calling the umontreal.ssj.probdist.ContinuousDistribution.inverseF method of the distribution object. Alternative generating methods are provided in subclasses.