/*
* 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.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.special.Beta;
import org.apache.commons.math3.util.FastMath;
/**
* Implementation of the F-distribution.
*
* @see <a href="http://en.wikipedia.org/wiki/F-distribution">F-distribution (Wikipedia)</a>
* @see <a href="http://mathworld.wolfram.com/F-Distribution.html">F-distribution (MathWorld)</a>
*/
public class FDistribution extends AbstractRealDistribution {
/**
* 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;
/** Cached numerical variance */
private double numericalVariance = Double.NaN;
/** Whether or not the numerical variance has been calculated */
private boolean numericalVarianceIsCalculated = false;
/**
* Creates an F distribution using the given degrees of freedom.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
* @throws NotStrictlyPositiveException if
* {@code numeratorDegreesOfFreedom <= 0} or
* {@code denominatorDegreesOfFreedom <= 0}.
*/
public FDistribution(double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom)
throws NotStrictlyPositiveException {
this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom,
DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates an F distribution using the given degrees of freedom
* and inverse cumulative probability accuracy.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates.
* @throws NotStrictlyPositiveException if
* {@code numeratorDegreesOfFreedom <= 0} or
* {@code denominatorDegreesOfFreedom <= 0}.
* @since 2.1
*/
public FDistribution(double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
this(new Well19937c(), numeratorDegreesOfFreedom,
denominatorDegreesOfFreedom, inverseCumAccuracy);
}
/**
* Creates an F distribution.
*
* @param rng Random number generator.
* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
* @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0} or
* {@code denominatorDegreesOfFreedom <= 0}.
* @since 3.3
*/
public FDistribution(RandomGenerator rng,
double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom)
throws NotStrictlyPositiveException {
this(rng, numeratorDegreesOfFreedom, denominatorDegreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates an F distribution.
*
* @param rng Random number generator.
* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates.
* @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0} or
* {@code denominatorDegreesOfFreedom <= 0}.
* @since 3.1
*/
public FDistribution(RandomGenerator rng,
double numeratorDegreesOfFreedom,
double denominatorDegreesOfFreedom,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
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;
}
/**
* {@inheritDoc}
*
* @since 2.1
*/
public double density(double x) {
return FastMath.exp(logDensity(x));
}
/** {@inheritDoc} **/
@Override
public double logDensity(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 nhalf * logn + nhalf * logx - logx +
mhalf * logm - nhalf * lognxm - mhalf * lognxm -
Beta.logBeta(nhalf, mhalf);
}
/**
* {@inheritDoc}
*
* 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>
*/
public double cumulativeProbability(double x) {
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;
}
/**
* Access the numerator degrees of freedom.
*
* @return the numerator degrees of freedom.
*/
public double getNumeratorDegreesOfFreedom() {
return numeratorDegreesOfFreedom;
}
/**
* Access the denominator degrees of freedom.
*
* @return the denominator degrees of freedom.
*/
public double getDenominatorDegreesOfFreedom() {
return denominatorDegreesOfFreedom;
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For denominator degrees of freedom parameter {@code b}, the mean is
* <ul>
* <li>if {@code b > 2} then {@code b / (b - 2)},</li>
* <li>else undefined ({@code Double.NaN}).
* </ul>
*/
public double getNumericalMean() {
final double denominatorDF = getDenominatorDegreesOfFreedom();
if (denominatorDF > 2) {
return denominatorDF / (denominatorDF - 2);
}
return Double.NaN;
}
/**
* {@inheritDoc}
*
* For numerator degrees of freedom parameter {@code a} and denominator
* degrees of freedom parameter {@code b}, the variance is
* <ul>
* <li>
* if {@code b > 4} then
* {@code [2 * b^2 * (a + b - 2)] / [a * (b - 2)^2 * (b - 4)]},
* </li>
* <li>else undefined ({@code Double.NaN}).
* </ul>
*/
public double getNumericalVariance() {
if (!numericalVarianceIsCalculated) {
numericalVariance = calculateNumericalVariance();
numericalVarianceIsCalculated = true;
}
return numericalVariance;
}
/**
* used by {@link #getNumericalVariance()}
*
* @return the variance of this distribution
*/
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}
*
* The lower bound of the support is always 0 no matter the parameters.
*
* @return lower bound of the support (always 0)
*/
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)
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return false;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}