Package org.apache.commons.statistics.distribution

Class FDistribution

java.lang.Object
org.apache.commons.statistics.distribution.FDistribution
All Implemented Interfaces:
ContinuousDistribution
public class FDistribution
extends java.lang.Object
Implementation of the F-distribution.
See Also:
F-distribution (Wikipedia), F-distribution (MathWorld)

  • Constructor Details

    • FDistribution

      public FDistribution​(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom)
      Creates a distribution.
      Parameters:
      numeratorDegreesOfFreedom - Numerator degrees of freedom.
      denominatorDegreesOfFreedom - Denominator degrees of freedom.
      Throws:
      java.lang.IllegalArgumentException - if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.

  • Method Details

    • 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 - Point at which the PDF is evaluated.
      Returns:
      the value of the probability density function at x.

    • logDensity

      public double logDensity​(double x)
      Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
      Parameters:
      x - Point at which the PDF is evaluated.
      Returns:
      the logarithm of the value of the probability density function at x.

    • 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
      Parameters:
      x - 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.

    • getMean

      public double getMean()
      Gets 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.

    • getVariance

      public double getVariance()
      Gets 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, or Double.NaN if it is not defined.

    • getSupportLowerBound

      public double getSupportLowerBound()
      Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. 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()
      Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. 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)

    • isSupportConnected

      public boolean isSupportConnected()
      Indicates 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

    • inverseCumulativeProbability

      public double inverseCumulativeProbability​(double p)
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
      • inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(X<=x) > 0} for p = 0.
      The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface ContinuousDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

    • sample

      public static double[] sample​(int n, ContinuousDistribution.Sampler sampler)
      Utility function for allocating an array and filling it with n samples generated by the given sampler.
      Parameters:
      n - Number of samples.
      sampler - Sampler.
      Returns:
      an array of size n.

    • createSampler

      public ContinuousDistribution.Sampler createSampler​(UniformRandomProvider rng)
      Creates a sampler.
      Specified by:
      createSampler in interface ContinuousDistribution
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.