Package org.apache.commons.math3.distribution

Class SaddlePointExpansion

  • final class SaddlePointExpansion
extends java.lang.Object

    Utility class used by various distributions to accurately compute their respective probability mass functions. The implementation for this class is based on the Catherine Loader's dbinom routines.

    This class is not intended to be called directly.

    References:

    1. Catherine Loader (2000). "Fast and Accurate Computation of Binomial Probabilities.". http://www.herine.net/stat/papers/dbinom.pdf

    Since:
    2.1

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private static double[] EXACT_STIRLING_ERRORS
      exact Stirling expansion error for certain values.
      private static double HALF_LOG_2_PI
      1/2 * log(2 π).

    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private SaddlePointExpansion()
      Default constructor.

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      (package private) static double getDeviancePart​(double x, double mu)
      A part of the deviance portion of the saddle point approximation.
      (package private) static double getStirlingError​(double z)
      Compute the error of Stirling's series at the given value.
      (package private) static double logBinomialProbability​(int x, int n, double p, double q)
      Compute the logarithm of the PMF for a binomial distribution using the saddle point expansion.

      • Methods inherited from class java.lang.Object

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

    • Field Detail

      • HALF_LOG_2_PI

        private static final double HALF_LOG_2_PI
        1/2 * log(2 π).

      • EXACT_STIRLING_ERRORS

        private static final double[] EXACT_STIRLING_ERRORS
        exact Stirling expansion error for certain values.

    • Constructor Detail

      • SaddlePointExpansion

        private SaddlePointExpansion()
        Default constructor.

    • Method Detail

      • getStirlingError

        static double getStirlingError​(double z)
        Compute the error of Stirling's series at the given value.

        References:

        1. Eric W. Weisstein. "Stirling's Series." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/StirlingsSeries.html

        Parameters:
        z - the value.
        Returns:
        the Striling's series error.

      • getDeviancePart

        static double getDeviancePart​(double x,
                              double mu)
        A part of the deviance portion of the saddle point approximation.

        References:

        1. Catherine Loader (2000). "Fast and Accurate Computation of Binomial Probabilities.". http://www.herine.net/stat/papers/dbinom.pdf

        Parameters:
        x - the x value.
        mu - the average.
        Returns:
        a part of the deviance.

      • logBinomialProbability

        static double logBinomialProbability​(int x,
                                     int n,
                                     double p,
                                     double q)
        Compute the logarithm of the PMF for a binomial distribution using the saddle point expansion.
        Parameters:
        x - the value at which the probability is evaluated.
        n - the number of trials.
        p - the probability of success.
        q - the probability of failure (1 - p).
        Returns:
        log(p(x)).