Package jsl.utilities.distributions

Class Beta

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.Beta

All Implemented Interfaces:

ControllableIfc, CDFIfc, ContinuousDistributionIfc, DistributionFunctionIfc, DistributionIfc, DomainIfc, InverseCDFIfc, MeanIfc, PDFIfc, VarianceIfc, GetNameIfc, IdentityIfc, NewInstanceIfc, ParametersIfc, GetRVariableIfc

public class Beta
extends Distribution
implements ContinuousDistributionIfc, InverseCDFIfc, GetRVariableIfc

The standard beta distribution defined over the range from (0,1)

Nested Class Summary

Nested classes/interfaces inherited from class jsl.utilities.distributions.Distribution

Distribution.RandomControls

Field Summary

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
Beta()	Creates a Beta with parameters 1.0, 1.0
Beta(double[] parameters)	Creates a beta with the supplied parameters
Beta(double alpha1, double alpha2)	Creates a beta with the supplied parameters
Beta(double alpha1, double alpha2, java.lang.String name)	Creates a beta with the supplied parameters

Method Summary

Modifier and Type	Method	Description
static double	approximateCDF(double pp, double qq, double a, double lnbeta)	Computes an approximation of the CDF for the Beta distribution Uses part of algorithm AS109, Applied Statistics, vol 26, no 1, 1977, pp 111-114
protected static double	betaContinuedFraction(double x, double a, double b)	Computes the continued fraction for the incomplete beta function.
static double	betaFunction(double z1, double z2)	Computes Beta(z1,z2)
double	cdf(double x)	Computes the CDF, has accuracy to about 10e-9
double	getAlpha1()
double	getAlpha2()
Interval	getDomain()
double	getMean()	Returns the mean or expected value of a distribution
double[]	getParameters()	Gets the parameters
RVariableIfc	getRandomVariable(RNStreamIfc rng)
double	getVariance()	Returns the variance of the distribution if defined
static double	incompleteBetaFunction(double x, double a, double b)	Computes the incomplete beta function at the supplied x Beta(x, a, b)/Beta(a, b)
double	invCDF(double p)	Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.
protected double	inverseBetaCDF(double p)	Computes the inverse of the beta CDF at the supplied probability point using an initial approximation and a root finding technique
static double	logBetaFunction(double z1, double z2)	The natural logarithm of Beta(z1,z2)
static void	main(java.lang.String[] args)
Beta	newInstance()	Returns a new instance
double	pdf(double x)	Returns the f(x) where f represents the probability density function for the distribution.
static double	regularizedIncompleteBetaFunction(double x, double a, double b)	Computes the regularized incomplete beta function at the supplied x
protected static double	regularizedIncompleteBetaFunction(double x, double a, double b, double lnbeta)	Computes the regularized incomplete beta function at the supplied x
static void	setContinuedFractionDesiredPrecision(double prec)	Sets the desired precision in the continued fraction expansion for the computation of the incompleteBetaFunction
static void	setContinuedFractionMaximumIterations(int maxIter)	Sets the maximum number of iterations in the continued fraction expansion for the computation of the incompleteBetaFunction
void	setParameters(double[] parameters)	Sets the parameters parameter[0] is alpha 1 parameter[1] is alpha 2
void	setParameters(double alpha1, double alpha2)	Changes the parameters to the supplied values
static void	setRootFindingDesiredPrecision(double prec)	Sets the desired precision of the root finding algorithm in the CDF inversion computation
static void	setRootFindingMaximumIterations(int maxIter)	Sets the maximum number of iterations of the root finding algorithm in the CDF inversion computation
java.lang.String	toString()

Methods inherited from class jsl.utilities.distributions.Distribution

getControls, getId, getName, getStandardDeviation, inverseContinuousCDFViaBisection, inverseContinuousCDFViaBisection, inverseDiscreteCDFViaSearchUp, setControls, setId, setName

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface jsl.utilities.distributions.CDFIfc

cdf, complementaryCDF

Methods inherited from interface jsl.utilities.random.rvariable.GetRVariableIfc

getRandomVariable, getRandomVariable

Constructor Detail

Beta

public Beta()

Creates a Beta with parameters 1.0, 1.0

Beta

public Beta(double alpha1,
            double alpha2)

Creates a beta with the supplied parameters

Parameters:

alpha1 - the alpha1 parameter

alpha2 - the alpha2 parameter

Beta

public Beta(double[] parameters)

Creates a beta with the supplied parameters

Parameters:

parameters - alpha1 is parameter[0], alpha2 is parameter[1]

Beta

public Beta(double alpha1,
            double alpha2,
            java.lang.String name)

Creates a beta with the supplied parameters

Parameters:

alpha1 - the alpha1 parameter

alpha2 - the alpha2 parameter

name - a label

Method Detail

newInstance

public final Beta newInstance()

Description copied from interface: NewInstanceIfc

Returns a new instance

Specified by:

newInstance in interface NewInstanceIfc

Specified by:

newInstance in class Distribution

Returns:

the new instance

getDomain

public final Interval getDomain()

Specified by:

getDomain in interface DomainIfc

getAlpha1

public final double getAlpha1()

Returns:

the first shape parameter

getAlpha2

public final double getAlpha2()

Returns:

the second shape parameter

setParameters

public final void setParameters(double alpha1,
                                double alpha2)

Changes the parameters to the supplied values

Parameters:

alpha1 - the alpha1 parameter

alpha2 - the alpha2 parameter

setParameters

public final void setParameters(double[] parameters)

Sets the parameters parameter[0] is alpha 1 parameter[1] is alpha 2

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - an array holding the parameters

getMean

public final double getMean()

Description copied from interface: MeanIfc

Returns the mean or expected value of a distribution

Specified by:

getMean in interface MeanIfc

Returns:

double the mean or expected value for the distribution

getParameters

public final double[] getParameters()

Description copied from interface: ParametersIfc

Gets the parameters

Specified by:

getParameters in interface ParametersIfc

Returns:

Returns an array of the parameters

getVariance

public final double getVariance()

Description copied from interface: VarianceIfc

Returns the variance of the distribution if defined

Specified by:

getVariance in interface VarianceIfc

Returns:

double the variance of the random variable

cdf

public double cdf(double x)

Computes the CDF, has accuracy to about 10e-9

Specified by:

cdf in interface CDFIfc

Parameters:

x - the x value to be evaluated

Returns:

a double representing the probability

invCDF

public double invCDF(double p)

Description copied from interface: InverseCDFIfc

Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.

Specified by:

invCDF in interface InverseCDFIfc

Parameters:

p - The probability to be evaluated for the inverse, p must be [0,1] or an IllegalArgumentException is thrown

Returns:

The inverse cdf evaluated at the supplied probability

pdf

public final double pdf(double x)

Description copied from interface: PDFIfc

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

Specified by:

pdf in interface PDFIfc

Parameters:

x - a double representing the value to be evaluated

Returns:

f(x)

betaFunction

public static double betaFunction(double z1,
                                  double z2)

Computes Beta(z1,z2)

Parameters:

z1 - the first parameter

z2 - the second parameter

Returns:

the computed value

logBetaFunction

public static double logBetaFunction(double z1,
                                     double z2)

The natural logarithm of Beta(z1,z2)

Parameters:

z1 - the first parameter

z2 - the second parameter

Returns:

natural logarithm of Beta(z1,z2)

incompleteBetaFunction

public static double incompleteBetaFunction(double x,
                                            double a,
                                            double b)

Computes the incomplete beta function at the supplied x Beta(x, a, b)/Beta(a, b)

Parameters:

x - the point to be evaluated

a - alpha 1

b - alpha 2

Returns:

the regularized beta function at the supplied x

regularizedIncompleteBetaFunction

public static double regularizedIncompleteBetaFunction(double x,
                                                       double a,
                                                       double b)

Computes the regularized incomplete beta function at the supplied x

Parameters:

x - the point to be evaluated

a - alpha 1

b - alpha 2

Returns:

the regularized incomplete beta function at the supplied x

regularizedIncompleteBetaFunction

protected static double regularizedIncompleteBetaFunction(double x,
                                                          double a,
                                                          double b,
                                                          double lnbeta)

Computes the regularized incomplete beta function at the supplied x

Parameters:

x - the point to be evaluated

a - alpha 1

b - alpha 2

lnbeta - the natural log of Beta(alpha1,alpha2)

Returns:

the regularized incomplete beta function at the supplied x

betaContinuedFraction

protected static double betaContinuedFraction(double x,
                                              double a,
                                              double b)

Computes the continued fraction for the incomplete beta function.

Parameters:

x - the point to be evaluated

a - alpha 1

b - alpha 2

Returns:

the continued fraction

inverseBetaCDF

protected final double inverseBetaCDF(double p)

Computes the inverse of the beta CDF at the supplied probability point using an initial approximation and a root finding technique

Parameters:

p - the probability to evaluate

Returns:

the inverse value

toString

public java.lang.String toString()

Overrides:

toString in class Distribution

approximateCDF

public static final double approximateCDF(double pp,
                                          double qq,
                                          double a,
                                          double lnbeta)

Computes an approximation of the CDF for the Beta distribution Uses part of algorithm AS109, Applied Statistics, vol 26, no 1, 1977, pp 111-114

Parameters:

pp - Alpha 1 parameter

qq - Alpha 2 parameter

a - The point to be evaluated

lnbeta - The log of Beta(alpha1,alpha2)

Returns:

the approx cdf value

setContinuedFractionDesiredPrecision

public static void setContinuedFractionDesiredPrecision(double prec)

Sets the desired precision in the continued fraction expansion for the computation of the incompleteBetaFunction

Parameters:

prec - the desired precision

setContinuedFractionMaximumIterations

public static void setContinuedFractionMaximumIterations(int maxIter)

Sets the maximum number of iterations in the continued fraction expansion for the computation of the incompleteBetaFunction

Parameters:

maxIter - the maximum number of iterations

setRootFindingDesiredPrecision

public static void setRootFindingDesiredPrecision(double prec)

Sets the desired precision of the root finding algorithm in the CDF inversion computation

Parameters:

prec - the desired precision

setRootFindingMaximumIterations

public static void setRootFindingMaximumIterations(int maxIter)

Sets the maximum number of iterations of the root finding algorithm in the CDF inversion computation

Parameters:

maxIter - the max iterations

getRandomVariable

public final RVariableIfc getRandomVariable(RNStreamIfc rng)

Specified by:

getRandomVariable in interface GetRVariableIfc

Overrides:

getRandomVariable in class Distribution

Parameters:

rng - the stream to use

Returns:

a random variable

main

public static void main(java.lang.String[] args)