/*
* 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.exception.NotStrictlyPositiveException;
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 $Id: FDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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 final double numeratorDegreesOfFreedom;
/** The numerator degrees of freedom. */
private final double denominatorDegreesOfFreedom;
/** Inverse cumulative probability accuracy. */
private final double solverAbsoluteAccuracy;
/**
* Create a F distribution using the given degrees of freedom.
* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
* @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0}
* or {@code denominatorDegreesOfFreedom <= 0}.
*/
public FDistributionImpl(double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom) {
this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom,
DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create an F distribution using the given degrees of freedom
* and inverse cumulative probability accuracy.
* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates.
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
* @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0}
* or {@code denominatorDegreesOfFreedom <= 0}.
* @since 2.1
*/
public FDistributionImpl(double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom,
double inverseCumAccuracy) {
if (numeratorDegreesOfFreedom <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
numeratorDegreesOfFreedom);
}
if (denominatorDegreesOfFreedom <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
denominatorDegreesOfFreedom);
}
this.numeratorDegreesOfFreedom = numeratorDegreesOfFreedom;
this.denominatorDegreesOfFreedom = 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, {@code X}, this method returns {@code P(X < x)}.
*
* The implementation of this method is based on
* <ul>
* <li>
* <a href="http://mathworld.wolfram.com/F-Distribution.html">
* F-Distribution</a>, equation (4).
* </li>
* </ul>
*
* @param x Value at which the CDF is evaluated.
* @return CDF for this distribution.
* @throws MathException if the cumulative probability cannot be
* computed due to convergence or other numerical errors.
*/
public double cumulativeProbability(double x) throws MathException {
double ret;
if (x <= 0) {
ret = 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, {@code X}, this method returns the critical
* point {@code x}, such that {@code P(X < x) = p}.
* Returns 0 when p = 0 and {@code Double.POSITIVE_INFINITY} when p = 1.
*
* @param p Desired probability.
* @return {@code x}, such that {@code P(X < x) = p}.
* @throws MathException if the inverse cumulative probability cannot be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if {@code p} is not a valid
* probability.
*/
@Override
public double inverseCumulativeProbability(final double p)
throws MathException {
if (p == 0) {
return 0;
}
if (p == 1) {
return Double.POSITIVE_INFINITY;
}
return super.inverseCumulativeProbability(p);
}
/**
* Access the domain value lower bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value lower bound, i.e. {@code P(X < 'lower bound') < p}.
*/
@Override
protected double getDomainLowerBound(double p) {
return 0;
}
/**
* Access the domain value upper bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value upper bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@Override
protected double getDomainUpperBound(double p) {
return Double.MAX_VALUE;
}
/**
* Access the initial domain value, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the initial domain value.
*/
@Override
protected double getInitialDomain(double p) {
double ret = 1;
double d = denominatorDegreesOfFreedom;
if (d > 2) {
// use mean
ret = d / (d - 2);
}
return ret;
}
/**
* {@inheritDoc}
*/
public double getNumeratorDegreesOfFreedom() {
return numeratorDegreesOfFreedom;
}
/**
* {@inheritDoc}
*/
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;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0 no matter the parameters.
*
* @return lower bound of the support (always 0)
*/
@Override
public double getSupportLowerBound() {
return 0;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity
* no matter the parameters.
*
* @return upper bound of the support (always Double.POSITIVE_INFINITY)
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* For denominator degrees of freedom parameter <code>b</code>,
* the mean is
* <ul>
* <li>if <code>b > 2</code> then <code>b / (b - 2)</code></li>
* <li>else <code>undefined</code>
* </ul>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalMean() {
final double denominatorDF = getDenominatorDegreesOfFreedom();
if (denominatorDF > 2) {
return denominatorDF / (denominatorDF - 2);
}
return Double.NaN;
}
/**
* {@inheritDoc}
*
* For numerator degrees of freedom parameter <code>a</code>
* and denominator degrees of freedom parameter <code>b</code>,
* the variance is
* <ul>
* <li>
* if <code>b > 4</code> then
* <code>[ 2 * b^2 * (a + b - 2) ] / [ a * (b - 2)^2 * (b - 4) ]</code>
* </li>
* <li>else <code>undefined</code>
* </ul>
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalVariance() {
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;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return true;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}