Package org.apache.commons.statistics.distribution

Class GammaDistribution

    • Constructor Summary

      Constructors 
      Constructor Description
      GammaDistribution​(double shape, double scale)
      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 getMean()
      Gets the mean of this distribution.
      double getScale()
      Returns the scale parameter of this distribution.
      double getShape()
      Returns the shape 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.
      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

    • Constructor Detail

      • GammaDistribution

        public GammaDistribution​(double shape,
                         double scale)
        Creates a distribution.
        Parameters:
        shape - the shape parameter
        scale - the scale parameter
        Throws:
        java.lang.IllegalArgumentException - if shape <= 0 or scale <= 0.

    • Method Detail

      • getShape

        public double getShape()
        Returns the shape parameter of this distribution.
        Returns:
        the shape parameter

      • getScale

        public double getScale()
        Returns 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.

      • 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. The implementation of this method is based on:
        • Chi-Squared Distribution, equation (9).
        • Casella, G., & Berger, R. (1990). Statistical Inference. Belmont, CA: Duxbury Press.
        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.

      • getMean

        public double getMean()
        Gets the mean of this distribution. For shape parameter alpha and scale parameter beta, the mean is alpha * beta.
        Returns:
        the mean, or Double.NaN if it is not defined.

      • getVariance

        public double getVariance()
        Gets the variance of this distribution. For shape parameter alpha and scale parameter beta, the variance is alpha * beta^2.
        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}. 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()
        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}. 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()
        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. The support of this distribution is connected.
        Returns:
        true

      • createSampler

        public ContinuousDistribution.Sampler createSampler​(UniformRandomProvider rng)
        Creates a sampler.

        Sampling algorithms:

        • For 0 < shape < 1:
          Ahrens, J. H. and Dieter, U., Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing, 12, 223-246, 1974.
        • For shape >= 1:
          Marsaglia and Tsang, A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, Volume 26 Issue 3, September, 2000.
        Specified by:
        createSampler in interface ContinuousDistribution
        Parameters:
        rng - Generator of uniformly distributed numbers.
        Returns:
        a sampler that produces random numbers according this distribution.

      • 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.