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## org.apache.commons.math.distribution
Class FDistributionImpl

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

All Implemented Interfaces:
  Serializable, ContinuousDistribution, Distribution, FDistribution

    public class FDistributionImpl

extends AbstractContinuousDistribution
implements FDistribution, Serializable

Default implementation of `FDistribution`.

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
`private double` | `denominatorDegreesOfFreedom` The numerator degrees of freedom
`private double` | `numeratorDegreesOfFreedom` The numerator degrees of freedom
`private static long` | `serialVersionUID` Serializable version identifier
`private double` | `solverAbsoluteAccuracy` Inverse cumulative probability accuracy

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

Constructor Summary
`FDistributionImpl(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom)` Create a F distribution using the given degrees of freedom.
`FDistributionImpl(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom, double inverseCumAccuracy)` Create a F distribution using the given degrees of freedom and inverse cumulative probability 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` | `getDenominatorDegreesOfFreedom()` Access the denominator 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` | `getNumeratorDegreesOfFreedom()` Access the numerator degrees of freedom.
`double` | `getNumericalMean()` Returns the mean of the distribution.
`double` | `getNumericalVariance()` Returns the variance of the distribution.
`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` | `setDenominatorDegreesOfFreedom(double degreesOfFreedom)` Deprecated. as of 2.1 (class will become immutable in 3.0)
`private void` | `setDenominatorDegreesOfFreedomInternal(double degreesOfFreedom)` Modify the denominator degrees of freedom.
`void` | `setNumeratorDegreesOfFreedom(double degreesOfFreedom)` Deprecated. as of 2.1 (class will become immutable in 3.0)
`private void` | `setNumeratorDegreesOfFreedomInternal(double degreesOfFreedom)` Modify the numerator degrees of freedom.

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

### serialVersionUID

    private static final long serialVersionUID

  Serializable version identifier

  See Also:
    Constant Field Values

### numeratorDegreesOfFreedom

    private double numeratorDegreesOfFreedom

  The numerator degrees of freedom

### denominatorDegreesOfFreedom

    private double denominatorDegreesOfFreedom

  The numerator degrees of freedom

### solverAbsoluteAccuracy

    private final double solverAbsoluteAccuracy

  Inverse cumulative probability accuracy

Constructor Detail

### FDistributionImpl

    public FDistributionImpl(double numeratorDegreesOfFreedom,
                             double denominatorDegreesOfFreedom)

  Create a F distribution using the given degrees of freedom.

  Parameters:
    `numeratorDegreesOfFreedom` - the numerator degrees of freedom.
    `denominatorDegreesOfFreedom` - the denominator degrees of freedom.

### FDistributionImpl

    public FDistributionImpl(double numeratorDegreesOfFreedom,
                             double denominatorDegreesOfFreedom,
                             double inverseCumAccuracy)

  Create a F distribution using the given degrees of freedom and inverse cumulative probability accuracy.

  Parameters:
    `numeratorDegreesOfFreedom` - the numerator degrees of freedom.
    `denominatorDegreesOfFreedom` - the denominator degrees of freedom.
    `inverseCumAccuracy` - the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`)
  Since:
    2.1

Method Detail

### 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). The implementation of this method is based on:
  - F-Distribution, equation (4).

  Specified by:
    `cumulativeProbability` in interface `Distribution`
  Parameters:
    `x` - the value at which the CDF is evaluated.
  Returns:
    CDF for this distribution.
  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 0 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

### setNumeratorDegreesOfFreedom

    @Deprecated
    public void setNumeratorDegreesOfFreedom(double degreesOfFreedom)

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

  Modify the numerator degrees of freedom.

  Specified by:
    `setNumeratorDegreesOfFreedom` in interface `FDistribution`
  Parameters:
    `degreesOfFreedom` - the new numerator degrees of freedom.
  Throws:
    `IllegalArgumentException` - if `degreesOfFreedom` is not positive.

### setNumeratorDegreesOfFreedomInternal

    private void setNumeratorDegreesOfFreedomInternal(double degreesOfFreedom)

  Modify the numerator degrees of freedom.

  Parameters:
    `degreesOfFreedom` - the new numerator degrees of freedom.
  Throws:
    `IllegalArgumentException` - if `degreesOfFreedom` is not positive.

### getNumeratorDegreesOfFreedom

    public double getNumeratorDegreesOfFreedom()

  Access the numerator degrees of freedom.

  Specified by:
    `getNumeratorDegreesOfFreedom` in interface `FDistribution`
  Returns:
    the numerator degrees of freedom.

### setDenominatorDegreesOfFreedom

    @Deprecated
    public void setDenominatorDegreesOfFreedom(double degreesOfFreedom)

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

  Modify the denominator degrees of freedom.

  Specified by:
    `setDenominatorDegreesOfFreedom` in interface `FDistribution`
  Parameters:
    `degreesOfFreedom` - the new denominator degrees of freedom.
  Throws:
    `IllegalArgumentException` - if `degreesOfFreedom` is not positive.

### setDenominatorDegreesOfFreedomInternal

    private void setDenominatorDegreesOfFreedomInternal(double degreesOfFreedom)

  Modify the denominator degrees of freedom.

  Parameters:
    `degreesOfFreedom` - the new denominator degrees of freedom.
  Throws:
    `IllegalArgumentException` - if `degreesOfFreedom` is not positive.

### getDenominatorDegreesOfFreedom

    public double getDenominatorDegreesOfFreedom()

  Access the denominator degrees of freedom.

  Specified by:
    `getDenominatorDegreesOfFreedom` in interface `FDistribution`
  Returns:
    the denominator degrees of freedom.

### 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 0, regardless of the parameters.

  Returns:
    lower bound of the support (always 0)
  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, regardless of the parameters.

  Returns:
    upper bound of the support (always Double.POSITIVE_INFINITY)
  Since:
    2.2

### getNumericalMean

    public double getNumericalMean()

  Returns the mean of the distribution. For denominator degrees of freedom parameter `b`, the mean is
  - if `b > 2` then `b / (b - 2)`
  - else `undefined`

  Returns:
    the mean
  Since:
    2.2

### getNumericalVariance

    public double getNumericalVariance()

  Returns the variance of the 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`

  Returns:
    the variance
  Since:
    2.2

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