org.apache.commons.math.distribution
Class TDistributionImpl

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

All Implemented Interfaces:

Serializable, ContinuousDistribution, Distribution, TDistribution

public class TDistributionImpl
extends AbstractContinuousDistribution
implements TDistribution, Serializable

Default implementation of TDistribution.

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

TDistributionImpl(double degreesOfFreedom)
Create a t distribution using the given degrees of freedom.

TDistributionImpl(double degreesOfFreedom, double inverseCumAccuracy)
Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.

Method Summary

double	cumulativeProbability(double x) For this distribution, X, this method returns P(X < x).
double	density(double x) Returns the probability density for a particular point.
double	getDegreesOfFreedom() Access the degrees of freedom.
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 the distribution.
double	getSupportUpperBound() Returns the upper bound of the support for the distribution.
double	inverseCumulativeProbability(double p) For this distribution, X, this method returns the critical point x, such that P(X < x) = p.
void	setDegreesOfFreedom(double degreesOfFreedom) 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 org.apache.commons.math.distribution.AbstractDistribution

cumulativeProbability

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math.distribution.Distribution

cumulativeProbability

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

TDistributionImpl

public TDistributionImpl(double degreesOfFreedom,
                         double inverseCumAccuracy)

Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.

Parameters:

degreesOfFreedom - the degrees of freedom.

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

Since:

2.1

TDistributionImpl

public TDistributionImpl(double degreesOfFreedom)

Create a t distribution using the given degrees of freedom.

Parameters:

degreesOfFreedom - the degrees of freedom.

Method Detail

setDegreesOfFreedom

@Deprecated
public void setDegreesOfFreedom(double degreesOfFreedom)

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

Modify the degrees of freedom.

Specified by:

setDegreesOfFreedom in interface TDistribution

Parameters:

degreesOfFreedom - the new degrees of freedom.

getDegreesOfFreedom

public double getDegreesOfFreedom()

Access the degrees of freedom.

Specified by:

getDegreesOfFreedom in interface TDistribution

Returns:

the degrees of freedom.

density

public double density(double x)

Returns 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

cumulativeProbability

public double cumulativeProbability(double x)
                             throws MathException

For this distribution, X, this method returns P(X < x).

Specified by:

cumulativeProbability in interface Distribution

Parameters:

x - the value at which the CDF is evaluated.

Returns:

CDF evaluated at x.

Throws:

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

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.

Returns Double.NEGATIVE_INFINITY for p=0 and Double.POSITIVE_INFINITY for p=1.

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.

IllegalArgumentException - if p is not a valid probability.

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 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 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

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 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

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 the distribution. The lower bound of the support is always negative infinity no matter the parameters.

Returns:

lower bound of the support (always Double.NEGATIVE_INFINITY)

Since:

2.2

getSupportUpperBound

public double getSupportUpperBound()

Returns the upper bound of the support for the distribution. The upper bound of the support is always positive infinity no matter the parameters.

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)

Since:

2.2

getNumericalMean

public double getNumericalMean()

Returns the mean. For degrees of freedom parameter df, the mean is

• if df > 1 then 0
• else undefined

Returns:

the mean

Since:

2.2

getNumericalVariance

public double getNumericalVariance()

Returns the variance. For degrees of freedom parameter df, the variance is

• if df > 2 then df / (df - 2)
• if 1 < df <= 2 then positive infinity
• else undefined

Returns:

the variance

Since:

2.2