Class LevyDistribution

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double c
      Scale parameter.
      private static double HALF_OVER_ERFCINV_HALF_SQUARED
      1 / 2(erfc^-1 (0.5))^2.
      private double halfC
      Half of c (for calculations).
      private double mu
      Location parameter.
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private LevyDistribution​(double mu, double c)  
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      ContinuousDistribution.Sampler createSampler​(org.apache.commons.rng.UniformRandomProvider rng)
      Creates a sampler.
      double cumulativeProbability​(double x)
      For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
      double density​(double x)
      Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
      double getLocation()
      Gets the location parameter of this distribution.
      double getMean()
      Gets the mean of this distribution.
      (package private) double getMedian()
      Gets the median.
      double getScale()
      Gets the scale parameter of this distribution.
      double getSupportLowerBound()
      Gets the lower bound of the support.
      double getSupportUpperBound()
      Gets the upper bound of the support.
      double getVariance()
      Gets the variance of this distribution.
      double inverseCumulativeProbability​(double p)
      Computes the quantile function of this distribution.
      double inverseSurvivalProbability​(double p)
      Computes the inverse survival probability function of this distribution.
      double logDensity​(double x)
      Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
      static LevyDistribution of​(double mu, double c)
      Creates a Levy distribution.
      double survivalProbability​(double x)
      For a random variable X whose values are distributed according to this distribution, this method returns P(X > x).
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Field Detail

      • HALF_OVER_ERFCINV_HALF_SQUARED

        private static final double HALF_OVER_ERFCINV_HALF_SQUARED
        1 / 2(erfc^-1 (0.5))^2. Computed using Matlab's VPA to 30 digits.
        See Also:
        Constant Field Values
      • mu

        private final double mu
        Location parameter.
      • c

        private final double c
        Scale parameter.
      • halfC

        private final double halfC
        Half of c (for calculations).
    • Constructor Detail

      • LevyDistribution

        private LevyDistribution​(double mu,
                                 double c)
        Parameters:
        mu - Location parameter.
        c - Scale parameter.
    • Method Detail

      • of

        public static LevyDistribution of​(double mu,
                                          double c)
        Creates a Levy distribution.
        Parameters:
        mu - Location parameter.
        c - Scale parameter.
        Returns:
        the distribution
        Throws:
        java.lang.IllegalArgumentException - if c <= 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.

        If x is less than the location parameter then 0 is returned, as in these cases the distribution is not defined.

        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.
        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.
      • 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:

        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 equal to positive infinity.

        Returns:
        positive infinity.
      • getVariance

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

        The variance is equal to positive infinity.

        Returns:
        positive infinity.
      • 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 the location.

        Returns:
        location.
      • 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.