jhplot.math.num.pdf
Class SaddlePoint
- java.lang.Object
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- jhplot.math.num.pdf.SaddlePoint
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public final class SaddlePoint 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:
- Catherine Loader (2000). "Fast and Accurate Computation of Binomial Probabilities.". http://www.herine.net/stat/papers/dbinom.pdf
- Since:
- 1.2
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Constructor Summary
Constructors Constructor and Description SaddlePoint()
Default constructor.
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Method Summary
All Methods Static Methods Concrete Methods 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.
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Method Detail
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getStirlingError
public static double getStirlingError(double z)
Compute the error of Stirling's series at the given value.References:
- 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.
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getDeviancePart
public static double getDeviancePart(double x, double mu)
A part of the deviance portion of the saddle point approximation.References:
- 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.
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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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