Class CauchyDistribution

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double location
      The location of this distribution.
      private double scale
      The scale of this distribution.
      private double scale2
      Density factor (scale^2).
      private double scaleOverPi
      Density factor (scale / pi).
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private CauchyDistribution​(double location, double scale)  
    • Field Detail

      • location

        private final double location
        The location of this distribution.
      • scale

        private final double scale
        The scale of this distribution.
      • scaleOverPi

        private final double scaleOverPi
        Density factor (scale / pi).
      • scale2

        private final double scale2
        Density factor (scale^2).
    • Constructor Detail

      • CauchyDistribution

        private CauchyDistribution​(double location,
                                   double scale)
        Parameters:
        location - Location parameter.
        scale - Scale parameter.
    • Method Detail

      • of

        public static CauchyDistribution of​(double location,
                                            double scale)
        Creates a Cauchy distribution.
        Parameters:
        location - Location parameter.
        scale - Scale parameter.
        Returns:
        the distribution
        Throws:
        java.lang.IllegalArgumentException - if scale <= 0.
      • getLocation

        public double getLocation()
        Gets the location parameter of this distribution.
        Returns:
        the location parameter.
      • getScale

        public double getScale()
        Gets the scale parameter of this distribution.
        Returns:
        the scale parameter.
      • 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.
      • 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 - 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.
      • survivalProbability

        public double survivalProbability​(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 complementary cumulative distribution function.

        By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

        Parameters:
        x - Point at which the survival function is evaluated.
        Returns:
        the probability that a random variable with this distribution takes a value greater than x.
      • cdf

        private static double cdf​(double x)
        Compute the CDF of the Cauchy distribution with location 0 and scale 1.
        Parameters:
        x - Point at which the CDF is evaluated
        Returns:
        CDF(x)
      • inverseSurvivalProbability

        public double inverseSurvivalProbability​(double p)
        Computes the inverse survival probability function of this distribution. For a random variable X distributed according to this distribution, the returned value is:

        \[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb R : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]

        By default, this is defined as inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.

        The default implementation returns:

        Returns Double.NEGATIVE_INFINITY when p == 1 and Double.POSITIVE_INFINITY when p == 0.

        Specified by:
        inverseSurvivalProbability in interface ContinuousDistribution
        Overrides:
        inverseSurvivalProbability in class AbstractContinuousDistribution
        Parameters:
        p - Survival probability.
        Returns:
        the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).
      • getMean

        public double getMean()
        Gets the mean of this distribution.

        The mean is always undefined.

        Returns:
        NaN.
      • getVariance

        public double getVariance()
        Gets the variance of this distribution.

        The variance is always undefined.

        Returns:
        NaN.
      • getSupportLowerBound

        public double getSupportLowerBound()
        Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. \( \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} \).

        The lower bound of the support is always negative infinity.

        Returns:
        negative infinity.
      • getSupportUpperBound

        public double getSupportUpperBound()
        Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. \( \inf \{ x \in \mathbb R : P(X \le x) = 1 \} \).

        The upper bound of the support is always positive infinity.

        Returns:
        positive infinity.