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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.math3.distribution; import org.apache.commons.math3.exception.NotStrictlyPositiveException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.special.Beta; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.random.RandomGenerator; import org.apache.commons.math3.random.Well19937c; /** * 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> * @version $Id: FDistribution.java 1416643 2012-12-03 19:37:14Z tn $ */ 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. * * @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. * * @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. * @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) { 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)); } /** * {@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; } }