Package org.apache.commons.statistics.distribution

Class BetaDistribution

    • Constructor Summary

      Constructors 
      Constructor Description
      BetaDistribution​(double alpha, double beta)
      Creates a new instance.

    • 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 getAlpha()
      Access the first shape parameter, alpha.
      double getBeta()
      Access the second shape parameter, beta.
      double getMean()
      Gets the mean 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

      • BetaDistribution

        public BetaDistribution​(double alpha,
                        double beta)
        Creates a new instance.
        Parameters:
        alpha - First shape parameter (must be positive).
        beta - Second shape parameter (must be positive).

    • Method Detail

      • getAlpha

        public double getAlpha()
        Access the first shape parameter, alpha.
        Returns:
        the first shape parameter.

      • getBeta

        public double getBeta()
        Access the second shape parameter, beta.
        Returns:
        the second shape 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.
        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 first shape parameter alpha and second shape parameter beta, the mean is alpha / (alpha + beta).
        Returns:
        the mean, or Double.NaN if it is not defined.

      • getVariance

        public double getVariance()
        Gets the variance of this distribution. For first shape parameter alpha and second shape parameter beta, the variance is (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)].
        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 1 no matter the parameters.
        Returns:
        upper bound of the support (always 1)

      • 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 is performed using Cheng's algorithm: 
         R. C. H. Cheng,
 "Generating beta variates with nonintegral shape parameters",
 Communications of the ACM, 21, 317-322, 1978.
        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.