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.

  Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

  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.

  Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

  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)
                throws NotStrictlyPositiveException

  Creates an F distribution.

  Parameters:

  rng - Random number generator.

  numeratorDegreesOfFreedom - Numerator degrees of freedom.

  denominatorDegreesOfFreedom - Denominator degrees of freedom.

  Throws:

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

  Since:

  3.3

• 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

• 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. 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. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double). The default implementation simply computes the logarithm of density(x).

  Overrides:

  logDensity in class AbstractRealDistribution

  Parameters:

  x - the point at which the PDF is evaluated

  Returns:

  the logarithm of the value of the probability density function at point 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

  • 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