jhplot.math.num.pdf
Class SaddlePoint

java.lang.Object
  extended by jhplot.math.num.pdf.SaddlePoint

public final class SaddlePoint
extends 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:
1.2

Constructor Summary
SaddlePoint()
          Default constructor.
 
Method Summary
static double getDeviancePart(double x, double mu)
          A part of the deviance portion of the saddle point approximation.
static double getStirlingError(double z)
          Compute the error of Stirling's series at the given value.
static double logBinomialProbability(int x, int n, double p, double q)
          Compute the PMF for a binomial distribution using the saddle point expansion.
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

SaddlePoint

public SaddlePoint()
Default constructor.

Method Detail

getStirlingError

public 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

public 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

public static double logBinomialProbability(int x,
                                            int n,
                                            double p,
                                            double q)
Compute 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)).


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