Package org.hipparchus.distribution.continuous

Class FDistribution

    • Constructor Detail

      • FDistribution

        public FDistribution​(double numeratorDegreesOfFreedom,
                     double denominatorDegreesOfFreedom)
              throws MathIllegalArgumentException
        Creates an F distribution using the given degrees of freedom.
        Parameters:
        numeratorDegreesOfFreedom - Numerator degrees of freedom.
        denominatorDegreesOfFreedom - Denominator degrees of freedom.
        Throws:
        MathIllegalArgumentException - if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.

      • FDistribution

        public FDistribution​(double numeratorDegreesOfFreedom,
                     double denominatorDegreesOfFreedom,
                     double inverseCumAccuracy)
              throws MathIllegalArgumentException
        Creates an F distribution.
        Parameters:
        numeratorDegreesOfFreedom - Numerator degrees of freedom.
        denominatorDegreesOfFreedom - Denominator degrees of freedom.
        inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates.
        Throws:
        MathIllegalArgumentException - if numeratorDegreesOfFreedom <= 0 or denominatorDegreesOfFreedom <= 0.

    • 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

      • 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).

        Specified by:
        logDensity in interface RealDistribution
        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
        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.

      • 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

      • 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)

      • 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