Class is obsolete.
This commit is contained in:
Gilles
parent
ef84681392
commit
87f6b2c3d2
|
|
@ -1,206 +0,0 @@
|
||||||
/*
|
|
||||||
* Licensed to the Apache Software Foundation (ASF) under one or more
|
|
||||||
* contributor license agreements. See the NOTICE file distributed with
|
|
||||||
* this work for additional information regarding copyright ownership.
|
|
||||||
* The ASF licenses this file to You under the Apache License, Version 2.0
|
|
||||||
* (the "License"); you may not use this file except in compliance with
|
|
||||||
* the License. You may obtain a copy of the License at
|
|
||||||
*
|
|
||||||
* http://www.apache.org/licenses/LICENSE-2.0
|
|
||||||
*
|
|
||||||
* Unless required by applicable law or agreed to in writing, software
|
|
||||||
* distributed under the License is distributed on an "AS IS" BASIS,
|
|
||||||
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
||||||
* See the License for the specific language governing permissions and
|
|
||||||
* limitations under the License.
|
|
||||||
*/
|
|
||||||
package org.apache.commons.math4.distribution;
|
|
||||||
|
|
||||||
import org.apache.commons.numbers.gamma.LogGamma;
|
|
||||||
import org.apache.commons.math4.util.FastMath;
|
|
||||||
import org.apache.commons.math4.util.MathUtils;
|
|
||||||
|
|
||||||
/**
|
|
||||||
* <p>
|
|
||||||
* 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 <a target="_blank"
|
|
||||||
* href="http://www.herine.net/stat/software/dbinom.html">dbinom</a> routines.
|
|
||||||
* </p>
|
|
||||||
* <p>
|
|
||||||
* This class is not intended to be called directly.
|
|
||||||
* </p>
|
|
||||||
* <p>
|
|
||||||
* References:
|
|
||||||
* <ol>
|
|
||||||
* <li>Catherine Loader (2000). "Fast and Accurate Computation of Binomial
|
|
||||||
* Probabilities.". <a target="_blank"
|
|
||||||
* href="http://www.herine.net/stat/papers/dbinom.pdf">
|
|
||||||
* http://www.herine.net/stat/papers/dbinom.pdf</a></li>
|
|
||||||
* </ol>
|
|
||||||
* </p>
|
|
||||||
*
|
|
||||||
* @since 2.1
|
|
||||||
*/
|
|
||||||
final class SaddlePointExpansion {
|
|
||||||
|
|
||||||
/** 1/2 * log(2 π). */
|
|
||||||
private static final double HALF_LOG_2_PI = 0.5 * FastMath.log(MathUtils.TWO_PI);
|
|
||||||
|
|
||||||
/** exact Stirling expansion error for certain values. */
|
|
||||||
private static final double[] EXACT_STIRLING_ERRORS = { 0.0, /* 0.0 */
|
|
||||||
0.1534264097200273452913848, /* 0.5 */
|
|
||||||
0.0810614667953272582196702, /* 1.0 */
|
|
||||||
0.0548141210519176538961390, /* 1.5 */
|
|
||||||
0.0413406959554092940938221, /* 2.0 */
|
|
||||||
0.03316287351993628748511048, /* 2.5 */
|
|
||||||
0.02767792568499833914878929, /* 3.0 */
|
|
||||||
0.02374616365629749597132920, /* 3.5 */
|
|
||||||
0.02079067210376509311152277, /* 4.0 */
|
|
||||||
0.01848845053267318523077934, /* 4.5 */
|
|
||||||
0.01664469118982119216319487, /* 5.0 */
|
|
||||||
0.01513497322191737887351255, /* 5.5 */
|
|
||||||
0.01387612882307074799874573, /* 6.0 */
|
|
||||||
0.01281046524292022692424986, /* 6.5 */
|
|
||||||
0.01189670994589177009505572, /* 7.0 */
|
|
||||||
0.01110455975820691732662991, /* 7.5 */
|
|
||||||
0.010411265261972096497478567, /* 8.0 */
|
|
||||||
0.009799416126158803298389475, /* 8.5 */
|
|
||||||
0.009255462182712732917728637, /* 9.0 */
|
|
||||||
0.008768700134139385462952823, /* 9.5 */
|
|
||||||
0.008330563433362871256469318, /* 10.0 */
|
|
||||||
0.007934114564314020547248100, /* 10.5 */
|
|
||||||
0.007573675487951840794972024, /* 11.0 */
|
|
||||||
0.007244554301320383179543912, /* 11.5 */
|
|
||||||
0.006942840107209529865664152, /* 12.0 */
|
|
||||||
0.006665247032707682442354394, /* 12.5 */
|
|
||||||
0.006408994188004207068439631, /* 13.0 */
|
|
||||||
0.006171712263039457647532867, /* 13.5 */
|
|
||||||
0.005951370112758847735624416, /* 14.0 */
|
|
||||||
0.005746216513010115682023589, /* 14.5 */
|
|
||||||
0.005554733551962801371038690 /* 15.0 */
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Default constructor.
|
|
||||||
*/
|
|
||||||
private SaddlePointExpansion() {
|
|
||||||
super();
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Compute the error of Stirling's series at the given value.
|
|
||||||
* <p>
|
|
||||||
* References:
|
|
||||||
* <ol>
|
|
||||||
* <li>Eric W. Weisstein. "Stirling's Series." From MathWorld--A Wolfram Web
|
|
||||||
* Resource. <a target="_blank"
|
|
||||||
* href="http://mathworld.wolfram.com/StirlingsSeries.html">
|
|
||||||
* http://mathworld.wolfram.com/StirlingsSeries.html</a></li>
|
|
||||||
* </ol>
|
|
||||||
* </p>
|
|
||||||
*
|
|
||||||
* @param z the value.
|
|
||||||
* @return the Striling's series error.
|
|
||||||
*/
|
|
||||||
static double getStirlingError(double z) {
|
|
||||||
double ret;
|
|
||||||
if (z < 15.0) {
|
|
||||||
double z2 = 2.0 * z;
|
|
||||||
if (FastMath.floor(z2) == z2) {
|
|
||||||
ret = EXACT_STIRLING_ERRORS[(int) z2];
|
|
||||||
} else {
|
|
||||||
ret = LogGamma.value(z + 1.0) - (z + 0.5) * FastMath.log(z) +
|
|
||||||
z - HALF_LOG_2_PI;
|
|
||||||
}
|
|
||||||
} else {
|
|
||||||
double z2 = z * z;
|
|
||||||
ret = (0.083333333333333333333 -
|
|
||||||
(0.00277777777777777777778 -
|
|
||||||
(0.00079365079365079365079365 -
|
|
||||||
(0.000595238095238095238095238 -
|
|
||||||
0.0008417508417508417508417508 /
|
|
||||||
z2) / z2) / z2) / z2) / z;
|
|
||||||
}
|
|
||||||
return ret;
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* A part of the deviance portion of the saddle point approximation.
|
|
||||||
* <p>
|
|
||||||
* References:
|
|
||||||
* <ol>
|
|
||||||
* <li>Catherine Loader (2000). "Fast and Accurate Computation of Binomial
|
|
||||||
* Probabilities.". <a target="_blank"
|
|
||||||
* href="http://www.herine.net/stat/papers/dbinom.pdf">
|
|
||||||
* http://www.herine.net/stat/papers/dbinom.pdf</a></li>
|
|
||||||
* </ol>
|
|
||||||
* </p>
|
|
||||||
*
|
|
||||||
* @param x the x value.
|
|
||||||
* @param mu the average.
|
|
||||||
* @return a part of the deviance.
|
|
||||||
*/
|
|
||||||
static double getDeviancePart(double x, double mu) {
|
|
||||||
double ret;
|
|
||||||
if (FastMath.abs(x - mu) < 0.1 * (x + mu)) {
|
|
||||||
double d = x - mu;
|
|
||||||
double v = d / (x + mu);
|
|
||||||
double s1 = v * d;
|
|
||||||
double s = Double.NaN;
|
|
||||||
double ej = 2.0 * x * v;
|
|
||||||
v *= v;
|
|
||||||
int j = 1;
|
|
||||||
while (s1 != s) {
|
|
||||||
s = s1;
|
|
||||||
ej *= v;
|
|
||||||
s1 = s + ej / ((j * 2) + 1);
|
|
||||||
++j;
|
|
||||||
}
|
|
||||||
ret = s1;
|
|
||||||
} else {
|
|
||||||
if (x == 0) {
|
|
||||||
return mu;
|
|
||||||
}
|
|
||||||
ret = x * FastMath.log(x / mu) + mu - x;
|
|
||||||
}
|
|
||||||
return ret;
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Compute the logarithm of the PMF for a binomial distribution
|
|
||||||
* using the saddle point expansion.
|
|
||||||
*
|
|
||||||
* @param x the value at which the probability is evaluated.
|
|
||||||
* @param n the number of trials.
|
|
||||||
* @param p the probability of success.
|
|
||||||
* @param q the probability of failure (1 - p).
|
|
||||||
* @return log(p(x)).
|
|
||||||
*/
|
|
||||||
static double logBinomialProbability(int x, int n, double p, double q) {
|
|
||||||
double ret;
|
|
||||||
if (x == 0) {
|
|
||||||
if (p < 0.1) {
|
|
||||||
ret = -getDeviancePart(n, n * q) - n * p;
|
|
||||||
} else {
|
|
||||||
if (n == 0) {
|
|
||||||
return 0;
|
|
||||||
}
|
|
||||||
ret = n * FastMath.log(q);
|
|
||||||
}
|
|
||||||
} else if (x == n) {
|
|
||||||
if (q < 0.1) {
|
|
||||||
ret = -getDeviancePart(n, n * p) - n * q;
|
|
||||||
} else {
|
|
||||||
ret = n * FastMath.log(p);
|
|
||||||
}
|
|
||||||
} else {
|
|
||||||
ret = getStirlingError(n) - getStirlingError(x) -
|
|
||||||
getStirlingError(n - x) - getDeviancePart(x, n * p) -
|
|
||||||
getDeviancePart(n - x, n * q);
|
|
||||||
double f = (MathUtils.TWO_PI * x * (n - x)) / n;
|
|
||||||
ret = -0.5 * FastMath.log(f) + ret;
|
|
||||||
}
|
|
||||||
return ret;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
Loading…
Reference in New Issue