Package org.apache.commons.statistics.distribution

Class LevyDistribution

java.lang.Object
org.apache.commons.statistics.distribution.LevyDistribution
All Implemented Interfaces:
ContinuousDistribution
public class LevyDistribution
extends java.lang.Object
This class implements the Lévy distribution.

  • Nested Class Summary

    Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

    ContinuousDistribution.Sampler

  • Constructor Summary

    Constructors 
    Constructor Description
    LevyDistribution​(double mu, double c)
    Creates a distribution.

  • Method Summary

    Modifier and Type Method Description
    ContinuousDistribution.Sampler createSampler​(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 the distribution.
    double getMean()
    Gets the mean of this distribution.
    double getScale()
    Gets the scale parameter of the 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.
    boolean isSupportConnected()
    Indicates whether the support is connected, i.e.
    double logDensity​(double x)
    Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
    static double[] sample​(int n, ContinuousDistribution.Sampler sampler)
    Utility function for allocating an array and filling it with n samples generated by the given sampler.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

    probability, probability

  • Constructor Details

    • LevyDistribution

      public LevyDistribution​(double mu, double c)
      Creates a distribution.
      Parameters:
      mu - location
      c - scale parameter

  • Method Details

    • 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.

      From Wikipedia: The probability density function of the Lévy distribution over the domain is

      f(x; μ, c) = √(c / 2π) * e-c / 2 (x - μ) / (x - μ)3/2

      For this distribution, X, this method returns P(X < x). If x is less than location parameter μ, Double.NaN 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. See documentation of density(double) for computation details.
      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.

      From Wikipedia: the cumulative distribution function is 

       f(x; u, c) = erfc (√ (c / 2 (x - u )))
      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.

    • inverseCumulativeProbability

      public double inverseCumulativeProbability​(double p)
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
      • inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(X<=x) > 0} for p = 0.
      The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface ContinuousDistribution
      Parameters:
      p - Cumulative probability.
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

    • getScale

      public double getScale()
      Gets the scale parameter of the distribution.
      Returns:
      scale parameter of the distribution

    • getLocation

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

    • getMean

      public double getMean()
      Gets the mean of this distribution.
      Returns:
      the mean, or Double.NaN if it is not defined.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution.
      Returns:
      the variance, or Double.NaN if it is not defined.

    • 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 R | P(X <= x) > 0}.
      Returns:
      the lower bound of the support.

    • 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 R | P(X <= x) = 1}.
      Returns:
      the upper bound of the support.

    • isSupportConnected

      public boolean isSupportConnected()
      Indicates whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.
      Returns:
      whether the support is connected.

    • sample

      public static double[] sample​(int n, ContinuousDistribution.Sampler sampler)
      Utility function for allocating an array and filling it with n samples generated by the given sampler.
      Parameters:
      n - Number of samples.
      sampler - Sampler.
      Returns:
      an array of size n.

    • createSampler

      public ContinuousDistribution.Sampler createSampler​(UniformRandomProvider rng)
      Creates a sampler.
      Specified by:
      createSampler in interface ContinuousDistribution
      Parameters:
      rng - Generator of uniformly distributed numbers.
      Returns:
      a sampler that produces random numbers according this distribution.