org.apache.commons.math.distribution
Class BetaDistributionImpl

java.lang.Object
  org.apache.commons.math.distribution.AbstractDistribution
      org.apache.commons.math.distribution.AbstractContinuousDistribution
          org.apache.commons.math.distribution.BetaDistributionImpl

All Implemented Interfaces:

Serializable, BetaDistribution, ContinuousDistribution, Distribution, HasDensity<Double>

public class BetaDistributionImpl
extends AbstractContinuousDistribution
implements BetaDistribution

Implements the Beta distribution.

References:

• Beta distribution

Since:

2.0

Version:

$Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $

See Also:

Serialized Form

Field Summary

static double

DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy

Fields inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

randomData

Constructor Summary

BetaDistributionImpl(double alpha, double beta)
Build a new instance.

BetaDistributionImpl(double alpha, double beta, double inverseCumAccuracy)
Build a new instance.

Method Summary

double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X ≤ x).
double	cumulativeProbability(double x0, double x1) For a random variable X whose values are distributed according to this distribution, this method returns P(x0 ≤ X ≤ x1).
double	density(double x) Return the probability density for a particular point.
double	density(Double x) Deprecated.
double	getAlpha() Access the shape parameter, alpha
double	getBeta() Access the shape parameter, beta
protected double	getDomainLowerBound(double p) Access the domain value lower bound, based on p, used to bracket a CDF root.
protected double	getDomainUpperBound(double p) Access the domain value upper bound, based on p, used to bracket a CDF root.
protected double	getInitialDomain(double p) Access the initial domain value, based on p, used to bracket a CDF root.
double	getNumericalMean() Returns the mean.
double	getNumericalVariance() Returns the variance.
protected double	getSolverAbsoluteAccuracy() Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
double	getSupportLowerBound() Returns the lower bound of the support for this distribution.
double	getSupportUpperBound() Returns the upper bound of the support for this distribution.
double	inverseCumulativeProbability(double p) For this distribution, X, this method returns the critical point x, such that P(X < x) = p.
void	setAlpha(double alpha) Deprecated. as of 2.1 (class will become immutable in 3.0)
void	setBeta(double beta) Deprecated. as of 2.1 (class will become immutable in 3.0)

Methods inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

reseedRandomGenerator, sample, sample

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy

Since:

2.1

See Also:

Constant Field Values

Constructor Detail

BetaDistributionImpl

public BetaDistributionImpl(double alpha,
                            double beta,
                            double inverseCumAccuracy)

Build a new instance.

Parameters:

alpha - first shape parameter (must be positive)

beta - second shape parameter (must be positive)

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY)

Since:

2.1

BetaDistributionImpl

public BetaDistributionImpl(double alpha,
                            double beta)

Build a new instance.

Parameters:

alpha - first shape parameter (must be positive)

beta - second shape parameter (must be positive)

Method Detail

setAlpha

@Deprecated
public void setAlpha(double alpha)

Deprecated. as of 2.1 (class will become immutable in 3.0)

Modify the shape parameter, alpha.

Specified by:

setAlpha in interface BetaDistribution

Parameters:

alpha - the new shape parameter.

getAlpha

public double getAlpha()

Access the shape parameter, alpha

Specified by:

getAlpha in interface BetaDistribution

Returns:

alpha.

setBeta

@Deprecated
public void setBeta(double beta)

Deprecated. as of 2.1 (class will become immutable in 3.0)

Modify the shape parameter, beta.

Specified by:

setBeta in interface BetaDistribution

Parameters:

beta - the new scale parameter.

getBeta

public double getBeta()

Access the shape parameter, beta

Specified by:

getBeta in interface BetaDistribution

Returns:

beta.

density

@Deprecated
public double density(Double x)

Deprecated.

Return the probability density for a particular point.

Specified by:

density in interface BetaDistribution

Specified by:

density in interface HasDensity<Double>

Parameters:

x - The point at which the density should be computed.

Returns:

The pdf at point x.

density

public double density(double x)

Return the probability density for a particular point.

Overrides:

density in class AbstractContinuousDistribution

Parameters:

x - The point at which the density should be computed.

Returns:

The pdf at point x.

Since:

2.1

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws MathException

For this distribution, X, this method returns the critical point x, such that P(X < x) = p.

Specified by:

inverseCumulativeProbability in interface ContinuousDistribution

Overrides:

inverseCumulativeProbability in class AbstractContinuousDistribution

Parameters:

p - the desired probability

Returns:

x, such that P(X < x) = p

Throws:

MathException - if the inverse cumulative probability can not be computed due to convergence or other numerical errors.

getInitialDomain

protected double getInitialDomain(double p)

Access the initial domain value, based on p, used to bracket a CDF root. This method is used by AbstractContinuousDistribution.inverseCumulativeProbability(double) to find critical values.

Specified by:

getInitialDomain in class AbstractContinuousDistribution

Parameters:

p - the desired probability for the critical value

Returns:

initial domain value

getDomainLowerBound

protected double getDomainLowerBound(double p)

Access the domain value lower bound, based on p, used to bracket a CDF root. This method is used by AbstractContinuousDistribution.inverseCumulativeProbability(double) to find critical values.

Specified by:

getDomainLowerBound in class AbstractContinuousDistribution

Parameters:

p - the desired probability for the critical value

Returns:

domain value lower bound, i.e. P(X < lower bound) < p

getDomainUpperBound

protected double getDomainUpperBound(double p)

Access the domain value upper bound, based on p, used to bracket a CDF root. This method is used by AbstractContinuousDistribution.inverseCumulativeProbability(double) to find critical values.

Specified by:

getDomainUpperBound in class AbstractContinuousDistribution

Parameters:

p - the desired probability for the critical value

Returns:

domain value upper bound, i.e. P(X < upper bound) > p

cumulativeProbability

public double cumulativeProbability(double x)
                             throws MathException

For a random variable X whose values are distributed according to this distribution, this method returns P(X ≤ x). In other words, this method represents the (cumulative) distribution function, or CDF, for this distribution.

Specified by:

cumulativeProbability in interface Distribution

Parameters:

x - the value at which the distribution function is evaluated.

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

Throws:

MathException - if the cumulative probability can not be computed due to convergence or other numerical errors.

cumulativeProbability

public double cumulativeProbability(double x0,
                                    double x1)
                             throws MathException

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 ≤ X ≤ x1).

The default implementation uses the identity

P(x0 ≤ X ≤ x1) = P(X ≤ x1) - P(X ≤ x0)

Specified by:

cumulativeProbability in interface Distribution

Overrides:

cumulativeProbability in class AbstractDistribution

Parameters:

x0 - the (inclusive) lower bound

x1 - the (inclusive) upper bound

Returns:

the probability that a random variable with this distribution will take a value between x0 and x1, including the endpoints.

Throws:

MathException - if the cumulative probability can not be computed due to convergence or other numerical errors.

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()

Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.

Overrides:

getSolverAbsoluteAccuracy in class AbstractContinuousDistribution

Returns:

the solver absolute accuracy

Since:

2.1

getSupportLowerBound

public double getSupportLowerBound()

Returns the lower bound of the support for this distribution. The support of the Beta distribution is always [0, 1], regardless of the parameters, so this method always returns 0.

Returns:

lower bound of the support (always 0)

Since:

2.2

getSupportUpperBound

public double getSupportUpperBound()

Returns the upper bound of the support for this distribution. The support of the Beta distribution is always [0, 1], regardless of the parameters, so this method always returns 1.

Returns:

lower bound of the support (always 1)

Since:

2.2

getNumericalMean

public double getNumericalMean()

Returns the mean. For first shape parameter s1 and second shape parameter s2, the mean is s1 / (s1 + s2)

Returns:

the mean

Since:

2.2

getNumericalVariance

public double getNumericalVariance()

Returns the variance. For first shape parameter s1 and second shape parameter s2, the variance is [ s1 * s2 ] / [ (s1 + s2)^2 * (s1 + s2 + 1) ]

Returns:

the variance

Since:

2.2