org.apache.commons.math3.distribution
Class FDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractRealDistribution
      org.apache.commons.math3.distribution.FDistribution

All Implemented Interfaces:

Serializable, RealDistribution

public class FDistribution
extends AbstractRealDistribution

Implementation of the F-distribution.

Version:

$Id: FDistribution.java 16735 2016-10-06 13:02:40Z bignon $

See Also:

F-distribution (Wikipedia), F-distribution (MathWorld), Serialized Form

Field Summary

static double

DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

FDistribution(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom)
Creates an F distribution using the given degrees of freedom.

FDistribution(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom, double inverseCumAccuracy)
Creates an F distribution using the given degrees of freedom and inverse cumulative probability accuracy.

FDistribution(RandomGenerator rng, double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom, double inverseCumAccuracy)
Creates an F distribution.

Method Summary

protected double	calculateNumericalVariance() used by getNumericalVariance()
double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getDenominatorDegreesOfFreedom() Access the denominator degrees of freedom.
double	getNumeratorDegreesOfFreedom() Access the numerator degrees of freedom.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
protected double	getSolverAbsoluteAccuracy() Returns the solver absolute accuracy for inverse cumulative computation.
double	getSupportLowerBound() Access the lower bound of the support.
double	getSupportUpperBound() Access the upper bound of the support.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
boolean	isSupportLowerBoundInclusive() Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive() Whether or not the upper bound of support is in the domain of the density function.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, inverseCumulativeProbability, probability, probability, 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

FDistribution

public FDistribution(double numeratorDegreesOfFreedom,
                     double denominatorDegreesOfFreedom)
              throws NotStrictlyPositiveException

Creates an F distribution using the given degrees of freedom.

Parameters:

numeratorDegreesOfFreedom - Numerator degrees of freedom.

denominatorDegreesOfFreedom - Denominator degrees of freedom.

Throws:

NotStrictlyPositiveException - if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.

FDistribution

public FDistribution(double numeratorDegreesOfFreedom,
                     double denominatorDegreesOfFreedom,
                     double inverseCumAccuracy)
              throws NotStrictlyPositiveException

Creates an F distribution using the given degrees of freedom and inverse cumulative probability accuracy.

Parameters:

numeratorDegreesOfFreedom - Numerator degrees of freedom.

denominatorDegreesOfFreedom - Denominator degrees of freedom.

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates.

Throws:

NotStrictlyPositiveException - if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.

Since:

2.1

FDistribution

public FDistribution(RandomGenerator rng,
                     double numeratorDegreesOfFreedom,
                     double denominatorDegreesOfFreedom,
                     double inverseCumAccuracy)
              throws NotStrictlyPositiveException

Creates an F distribution.

Parameters:

rng - Random number generator.

numeratorDegreesOfFreedom - Numerator degrees of freedom.

denominatorDegreesOfFreedom - Denominator degrees of freedom.

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates.

Throws:

NotStrictlyPositiveException - if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.

Since:

3.1

Method Detail

density

public double density(double x)

Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

Since:

2.1

cumulativeProbability

public double cumulativeProbability(double x)

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 (CDF) for this distribution. The implementation of this method is based on

• F-Distribution, equation (4).

Parameters:

x - the point at which the CDF is evaluated

Returns:

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

getNumeratorDegreesOfFreedom

public double getNumeratorDegreesOfFreedom()

Access the numerator degrees of freedom.

Returns:

the numerator degrees of freedom.

getDenominatorDegreesOfFreedom

public double getDenominatorDegreesOfFreedom()

Access the denominator degrees of freedom.

Returns:

the denominator degrees of freedom.

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:

getSolverAbsoluteAccuracy in class AbstractRealDistribution

Returns:

the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For denominator degrees of freedom parameter b, the mean is

• if b > 2 then b / (b - 2),
• else undefined (Double.NaN).

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For numerator degrees of freedom parameter a and denominator degrees of freedom parameter b, the variance is

• if b > 4 then [2 * b^2 * (a + b - 2)] / [a * (b - 2)^2 * (b - 4)],
• else undefined (Double.NaN).

Returns:

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

calculateNumericalVariance

protected double calculateNumericalVariance()

used by getNumericalVariance()

Returns:

the variance of this distribution

getSupportLowerBound

public double getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always 0 no matter the parameters.

Returns:

lower bound of the support (always 0)

getSupportUpperBound

public double getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

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

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:

true