jhplot.math.num.pdf

Class SaddlePoint

java.lang.Object

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

Constructors

Constructor and Description
SaddlePoint() Default constructor.

Method Summary

Modifier and Type	Method and Description
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)).