/* * 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: *
p
.
*
* Returns 0 for p=0 and Double.POSITIVE_INFINITY
for p=1.
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
* b > 2
then b / (b - 2)
undefined
* a
* and denominator degrees of freedom parameter b
,
* the variance is
* b > 4
then
* [ 2 * b^2 * (a + b - 2) ] / [ a * (b - 2)^2 * (b - 4) ]
* undefined
*