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/*
* 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.math.distribution;
import java.io.Serializable;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.special.Beta;
import org.apache.commons.math.util.FastMath;
/**
* Default implementation of
* {@link org.apache.commons.math.distribution.FDistribution}.
*
* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
*/
public class FDistributionImpl
extends AbstractContinuousDistribution
implements FDistribution, Serializable {
/**
* Default inverse cumulative probability accuracy
* @since 2.1
*/
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
/** Serializable version identifier */
private static final long serialVersionUID = -8516354193418641566L;
/** The numerator degrees of freedom*/
private double numeratorDegreesOfFreedom;
/** The numerator degrees of freedom*/
private double denominatorDegreesOfFreedom;
/** Inverse cumulative probability accuracy */
private final double solverAbsoluteAccuracy;
/**
* Create a F distribution using the given degrees of freedom.
* @param numeratorDegreesOfFreedom the numerator degrees of freedom.
* @param denominatorDegreesOfFreedom the denominator degrees of freedom.
*/
public FDistributionImpl(double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom) {
this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a F distribution using the given degrees of freedom and inverse cumulative probability accuracy.
* @param numeratorDegreesOfFreedom the numerator degrees of freedom.
* @param denominatorDegreesOfFreedom the denominator degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @since 2.1
*/
public FDistributionImpl(double numeratorDegreesOfFreedom, double denominatorDegreesOfFreedom,
double inverseCumAccuracy) {
super();
setNumeratorDegreesOfFreedomInternal(numeratorDegreesOfFreedom);
setDenominatorDegreesOfFreedomInternal(denominatorDegreesOfFreedom);
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Returns the probability density for a particular point.
*
* @param x The point at which the density should be computed.
* @return The pdf at point x.
* @since 2.1
*/
@Override
public double density(double x) {
final double nhalf = numeratorDegreesOfFreedom / 2;
final double mhalf = denominatorDegreesOfFreedom / 2;
final double logx = FastMath.log(x);
final double logn = FastMath.log(numeratorDegreesOfFreedom);
final double logm = FastMath.log(denominatorDegreesOfFreedom);
final double lognxm = FastMath.log(numeratorDegreesOfFreedom * x + denominatorDegreesOfFreedom);
return FastMath.exp(nhalf*logn + nhalf*logx - logx + mhalf*logm - nhalf*lognxm -
mhalf*lognxm - Beta.logBeta(nhalf, mhalf));
}
/**
* For this distribution, X, this method returns P(X < x).
*
* The implementation of this method is based on:
*
* -
*
* F-Distribution, equation (4).
*
*
* @param x the value at which the CDF is evaluated.
* @return CDF for this distribution.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
public double cumulativeProbability(double x) throws MathException {
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
double n = numeratorDegreesOfFreedom;
double m = denominatorDegreesOfFreedom;
ret = Beta.regularizedBeta((n * x) / (m + n * x),
0.5 * n,
0.5 * m);
}
return ret;
}
/**
* For this distribution, X, this method returns the critical point x, such
* that P(X < x) = p.
*
* Returns 0 for p=0 and Double.POSITIVE_INFINITY for p=1.
*
* @param p the desired probability
* @return x, such that P(X < x) = p
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if p is not a valid
* probability.
*/
@Override
public double inverseCumulativeProbability(final double p)
throws MathException {
if (p == 0) {
return 0d;
}
if (p == 1) {
return Double.POSITIVE_INFINITY;
}
return super.inverseCumulativeProbability(p);
}
/**
* Access the domain value lower bound, based on p, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < lower bound) < p
*/
@Override
protected double getDomainLowerBound(double p) {
return 0.0;
}
/**
* Access the domain value upper bound, based on p, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < upper bound) > p
*/
@Override
protected double getDomainUpperBound(double p) {
return Double.MAX_VALUE;
}
/**
* Access the initial domain value, based on p, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return initial domain value
*/
@Override
protected double getInitialDomain(double p) {
double ret = 1.0;
double d = denominatorDegreesOfFreedom;
if (d > 2.0) {
// use mean
ret = d / (d - 2.0);
}
return ret;
}
/**
* Modify the numerator degrees of freedom.
* @param degreesOfFreedom the new numerator degrees of freedom.
* @throws IllegalArgumentException if degreesOfFreedom is not
* positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setNumeratorDegreesOfFreedom(double degreesOfFreedom) {
setNumeratorDegreesOfFreedomInternal(degreesOfFreedom);
}
/**
* Modify the numerator degrees of freedom.
* @param degreesOfFreedom the new numerator degrees of freedom.
* @throws IllegalArgumentException if degreesOfFreedom is not
* positive.
*/
private void setNumeratorDegreesOfFreedomInternal(double degreesOfFreedom) {
if (degreesOfFreedom <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, degreesOfFreedom);
}
this.numeratorDegreesOfFreedom = degreesOfFreedom;
}
/**
* Access the numerator degrees of freedom.
* @return the numerator degrees of freedom.
*/
public double getNumeratorDegreesOfFreedom() {
return numeratorDegreesOfFreedom;
}
/**
* Modify the denominator degrees of freedom.
* @param degreesOfFreedom the new denominator degrees of freedom.
* @throws IllegalArgumentException if degreesOfFreedom is not
* positive.
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setDenominatorDegreesOfFreedom(double degreesOfFreedom) {
setDenominatorDegreesOfFreedomInternal(degreesOfFreedom);
}
/**
* Modify the denominator degrees of freedom.
* @param degreesOfFreedom the new denominator degrees of freedom.
* @throws IllegalArgumentException if degreesOfFreedom is not
* positive.
*/
private void setDenominatorDegreesOfFreedomInternal(double degreesOfFreedom) {
if (degreesOfFreedom <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM, degreesOfFreedom);
}
this.denominatorDegreesOfFreedom = degreesOfFreedom;
}
/**
* Access the denominator degrees of freedom.
* @return the denominator degrees of freedom.
*/
public double getDenominatorDegreesOfFreedom() {
return denominatorDegreesOfFreedom;
}
/**
* Return the absolute accuracy setting of the solver used to estimate
* inverse cumulative probabilities.
*
* @return the solver absolute accuracy
* @since 2.1
*/
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* Returns the lower bound of the support for the distribution.
*
* The lower bound of the support is always 0, regardless of the parameters.
*
* @return lower bound of the support (always 0)
* @since 2.2
*/
public double getSupportLowerBound() {
return 0;
}
/**
* Returns the upper bound of the support for the distribution.
*
* The upper bound of the support is always positive infinity,
* regardless of the parameters.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
* @since 2.2
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* Returns the mean of the distribution.
*
* For denominator degrees of freedom parameter b,
* the mean is
*
* - if
b > 2 then b / (b - 2)
* - else
undefined
*
*
* @return the mean
* @since 2.2
*/
public double getNumericalMean() {
final double denominatorDF = getDenominatorDegreesOfFreedom();
if (denominatorDF > 2) {
return denominatorDF / (denominatorDF - 2);
}
return Double.NaN;
}
/**
* Returns the variance of the distribution.
*
* For numerator degrees of freedom parameter a
* and denominator degrees of freedom parameter b,
* the variance is
*
* -
* if
b > 4 then
* [ 2 * b^2 * (a + b - 2) ] / [ a * (b - 2)^2 * (b - 4) ]
*
* - else
undefined
*
*
* @return the variance
* @since 2.2
*/
public double getNumericalVariance() {
final double denominatorDF = getDenominatorDegreesOfFreedom();
if (denominatorDF > 4) {
final double numeratorDF = getNumeratorDegreesOfFreedom();
final double denomDFMinusTwo = denominatorDF - 2;
return ( 2 * (denominatorDF * denominatorDF) * (numeratorDF + denominatorDF - 2) ) /
( (numeratorDF * (denomDFMinusTwo * denomDFMinusTwo) * (denominatorDF - 4)) );
}
return Double.NaN;
}
}
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