java.lang.Object
- cern.colt.PersistentObject
- - cern.jet.random.AbstractDistribution
  - - cern.jet.random.AbstractContinousDistribution
    - - cern.jet.random.Beta

All Implemented Interfaces:

DoubleFunction, IntFunction, java.io.Serializable, java.lang.Cloneable
```
public class Beta
extends AbstractContinousDistribution
```
Beta distribution; math definition and animated definition.
p(x) = k * x^(alpha-1) * (1-x)^(beta-1) with k = g(alpha+beta)/(g(alpha)*g(beta)) and g(a) being the gamma function.
Valid parameter ranges: alpha > 0 and beta > 0.
Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.
Static methods operate on a default uniform random number generator; they are synchronized.
Implementation:
Method: Stratified Rejection/Patchwork Rejection. High performance implementation.
This is a port of bsprc.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon
H. Sakasegawa (1983): Stratified rejection and squeeze method for generating beta random numbers, Ann. Inst. Statist. Math. 35 B, 291-302.
and
Stadlober E., H. Zechner (1993), Generating beta variates via patchwork rejection,, Computing 50, 1-18.

Version:

1.0, 09/24/99

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field	Description
`(package private) double`	`a`
`(package private) double`	`a_`
`(package private) double`	`a_last`
`protected double`	`alpha`
`(package private) double`	`b`
`(package private) double`	`b_`
`(package private) double`	`b_last`
`protected double`	`beta`
`(package private) double`	`c`
`(package private) double`	`D`
`(package private) double`	`Dl`
`(package private) double`	`f1`
`(package private) double`	`f2`
`(package private) double`	`f4`
`(package private) double`	`f5`
`(package private) double`	`fa`
`(package private) double`	`fb`
`(package private) double`	`ll`
`(package private) double`	`lr`
`(package private) double`	`m`
`(package private) double`	`ml`
`(package private) double`	`mu`
`(package private) double`	`p_last`
`(package private) double`	`p1`
`(package private) double`	`p2`
`(package private) double`	`p3`
`(package private) double`	`p4`
`(package private) double`	`PDF_CONST`
`(package private) double`	`q_last`
`(package private) double`	`s`
`protected static Beta`	`shared`
`(package private) double`	`t`
`(package private) double`	`x1`
`(package private) double`	`x2`
`(package private) double`	`x4`
`(package private) double`	`x5`
`(package private) double`	`z2`
`(package private) double`	`z4`

Fields inherited from class cern.jet.random.AbstractDistribution
randomGenerator

Fields inherited from class cern.colt.PersistentObject
serialVersionUID

Constructor Summary

Constructors
Constructor Description

Beta(double alpha, double beta, RandomEngine randomGenerator)
Constructs a Beta distribution.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`protected double`	`b00(double a, double b, RandomEngine randomGenerator)`
`protected double`	`b01(double a, double b, RandomEngine randomGenerator)`
`protected double`	`b1prs(double p, double q, RandomEngine randomGenerator)`
`double`	`cdf(double x)`	Returns the cumulative distribution function.
`private static double`	`f(double x, double a, double b, double m)`
`double`	`nextDouble()`	Returns a random number from the distribution.
`double`	`nextDouble(double alpha, double beta)`	Returns a beta distributed random number; bypasses the internal state.
`double`	`pdf(double x)`	Returns the cumulative distribution function.
`void`	`setState(double alpha, double beta)`	Sets the parameters.
`static double`	`staticNextDouble(double alpha, double beta)`	Returns a random number from the distribution.
`java.lang.String`	`toString()`	Returns a String representation of the receiver.
`private static void`	`xstaticSetRandomGenerator(RandomEngine randomGenerator)`	Sets the uniform random number generated shared by all static methods.

Methods inherited from class cern.jet.random.AbstractDistribution
apply, apply, clone, getRandomGenerator, makeDefaultGenerator, nextInt, setRandomGenerator

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

Field Detail

alpha
```
protected double alpha
```

beta
```
protected double beta
```

PDF_CONST
```
double PDF_CONST
```

a_last
```
double a_last
```

b_last
```
double b_last
```

a_
```
double a_
```

b_
```
double b_
```

t
```
double t
```

fa
```
double fa
```

fb
```
double fb
```

p1
```
double p1
```

p2
```
double p2
```

c
```
double c
```

ml
```
double ml
```

mu
```
double mu
```

p_last
```
double p_last
```

q_last
```
double q_last
```

a
```
double a
```

b
```
double b
```

s
```
double s
```

m
```
double m
```

D
```
double D
```

Dl
```
double Dl
```

x1
```
double x1
```

x2
```
double x2
```

x4
```
double x4
```

x5
```
double x5
```

f1
```
double f1
```

f2
```
double f2
```

f4
```
double f4
```

f5
```
double f5
```

ll
```
double ll
```

lr
```
double lr
```

z2
```
double z2
```

z4
```
double z4
```

p3
```
double p3
```

p4
```
double p4
```

shared
```
protected static Beta shared
```

Constructor Detail

Beta

public Beta(double alpha,
            double beta,
            RandomEngine randomGenerator)

Constructs a Beta distribution.

Method Detail

b00

protected double b00(double a,
                     double b,
                     RandomEngine randomGenerator)

b01

protected double b01(double a,
                     double b,
                     RandomEngine randomGenerator)

b1prs

protected double b1prs(double p,
                       double q,
                       RandomEngine randomGenerator)

cdf
```
public double cdf(double x)
```
Returns the cumulative distribution function.

f

private static double f(double x,
                        double a,
                        double b,
                        double m)

nextDouble
```
public double nextDouble()
```
Returns a random number from the distribution.

Specified by:

nextDouble in class AbstractDistribution

nextDouble

public double nextDouble(double alpha,
                         double beta)

Returns a beta distributed random number; bypasses the internal state.

pdf
```
public double pdf(double x)
```
Returns the cumulative distribution function.

setState

public void setState(double alpha,
                     double beta)

Sets the parameters.

staticNextDouble

public static double staticNextDouble(double alpha,
                                      double beta)

Returns a random number from the distribution.

toString
```
public java.lang.String toString()
```
Returns a String representation of the receiver.

Overrides:

toString in class java.lang.Object

xstaticSetRandomGenerator
```
private static void xstaticSetRandomGenerator(RandomEngine randomGenerator)
```
Sets the uniform random number generated shared by all static methods.

Parameters:

randomGenerator - the new uniform random number generator to be shared.

Class Beta

Field Summary

Fields inherited from class cern.jet.random.AbstractDistribution

Fields inherited from class cern.colt.PersistentObject

Constructor Summary

Method Summary

Methods inherited from class cern.jet.random.AbstractDistribution

Methods inherited from class java.lang.Object

Field Detail

alpha

beta

PDF_CONST

a_last

b_last

a_

b_

t

fa

fb

p1

p2

c

ml

mu

p_last

q_last

a

b

s

m

D

Dl

x1

x2

x4

x5

f1

f2

f4

f5

ll

lr

z2

z4

p3

p4

shared

Constructor Detail

Beta

Method Detail

b00

b01

b1prs

cdf

f

nextDouble

nextDouble

pdf

setState

staticNextDouble

toString

xstaticSetRandomGenerator