Package org.hipparchus.distribution.continuous

Class ChiSquaredDistribution

    • Constructor Detail

      • ChiSquaredDistribution

        public ChiSquaredDistribution​(double degreesOfFreedom)
        Create a Chi-Squared distribution with the given degrees of freedom.
        Parameters:
        degreesOfFreedom - Degrees of freedom.

      • ChiSquaredDistribution

        public ChiSquaredDistribution​(double degreesOfFreedom,
                              double inverseCumAccuracy)
        Create a Chi-Squared distribution with the given degrees of freedom and inverse cumulative probability accuracy.
        Parameters:
        degreesOfFreedom - Degrees of freedom.
        inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to AbstractRealDistribution.DEFAULT_SOLVER_ABSOLUTE_ACCURACY).

    • Method Detail

      • getDegreesOfFreedom

        public double getDegreesOfFreedom()
        Access the number of degrees of freedom.
        Returns:
        the degrees of freedom.

      • 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.
        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

      • getNumericalMean

        public double getNumericalMean()
        Use this method to get the numerical value of the mean of this distribution. For k degrees of freedom, the mean is k.
        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.
        Returns:
        2 * k, where k is the number of degrees of freedom.

      • 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 degrees of freedom.
        Returns:
        zero.

      • 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 degrees of freedom.
        Returns:
        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