Package org.apache.commons.statistics.distribution

Class SaddlePointExpansionUtils

  • final class SaddlePointExpansionUtils
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.

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private static double[] EXACT_STIRLING_ERRORS
      Exact Stirling expansion error for certain values.
      private static double ONE_TENTH
      1/10.
      private static int STIRLING_ERROR_THRESHOLD
      The threshold value for switching the method to compute th Stirling error.
      private static double TWO_PI
      2 π.

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      (package private) static double getDeviancePart​(int x, double mu)
      A part of the deviance portion of the saddle point approximation.
      (package private) static double getStirlingError​(int 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

      • STIRLING_ERROR_THRESHOLD

        private static final int STIRLING_ERROR_THRESHOLD
        The threshold value for switching the method to compute th Stirling error.
        See Also:
        Constant Field Values

      • EXACT_STIRLING_ERRORS

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

    • Constructor Detail

      • SaddlePointExpansionUtils

        private SaddlePointExpansionUtils()
        Forbid construction.

    • Method Detail

      • getStirlingError

        static double getStirlingError​(int 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. https://mathworld.wolfram.com/StirlingsSeries.html

        Note: This function has been modified for integer z.

        Parameters:
        z - Value at which the function is evaluated.
        Returns:
        the Stirling's series error.

      • getDeviancePart

        static double getDeviancePart​(int 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

        Note: This function has been modified for integer x.

        Parameters:
        x - Value at which the function is evaluated.
        mu - 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 - Value at which the probability is evaluated.
        n - Number of trials.
        p - Probability of success.
        q - Probability of failure (1 - p).
        Returns:
        log(p(x)).