Class SaddlePointExpansion
- java.lang.Object
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- org.apache.commons.math3.distribution.SaddlePointExpansion
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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:
- Catherine Loader (2000). "Fast and Accurate Computation of Binomial Probabilities.". http://www.herine.net/stat/papers/dbinom.pdf
- Since:
- 2.1
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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).
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Constructor Summary
Constructors Modifier Constructor Description private
SaddlePointExpansion()
Default constructor.
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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.
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Method Detail
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getStirlingError
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
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
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)).
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