/* * 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.ConvergenceException; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.MathException; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.analysis.UnivariateRealFunction; import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils; /** * Base class for continuous distributions. Default implementations are * provided for some of the methods that do not vary from distribution to * distribution. * * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $ */ public abstract class AbstractContinuousDistribution extends AbstractDistribution implements ContinuousDistribution, Serializable { /** * Serializable version identifier */ private static final long serialVersionUID = -38038050983108802L; /** * Solver absolute accuracy for inverse cum computation * * @since 2.1 */ private double solverAbsoluteAccuracy = 1E-6; /** * Default constructor. */ protected AbstractContinuousDistribution() { super(); } /** * Return the probability density for a particular point. * * @param x The point at which the density should be computed. * @return The pdf at point x. * @throws MathRuntimeException if the specialized class hasn't implemented this function * @since 2.1 */ @Override public double density(double x) throws MathRuntimeException { throw new MathRuntimeException(new UnsupportedOperationException(), "This distribution does not have a density function implemented"); } @Override public double logDensity(double x) { return Math.log(density(x)); } /** * For this distribution, X, this method returns the critical point x, such * that P(X < x) = <code>p</code>. * * @param p the desired probability * @return x, such that P(X < x) = <code>p</code> * @throws MathException if the inverse cumulative probability can not be * computed due to convergence or other numerical errors. * @throws IllegalArgumentException if <code>p</code> is not a valid * probability. */ @Override public double inverseCumulativeProbability(final double p) throws MathException { if (p < 0.0 || p > 1.0) { throw MathRuntimeException.createIllegalArgumentException( "{0} out of [{1}, {2}] range", p, 0.0, 1.0); } // by default, do simple root finding using bracketing and default solver. // subclasses can override if there is a better method. UnivariateRealFunction rootFindingFunction = new UnivariateRealFunction() { @Override public double value(double x) throws FunctionEvaluationException { double ret = Double.NaN; try { ret = cumulativeProbability(x) - p; } catch (MathException ex) { throw new FunctionEvaluationException(ex, x, ex.getPattern(), ex.getArguments()); } if (Double.isNaN(ret)) { throw new FunctionEvaluationException(x, "Cumulative probability function returned NaN for argument {0} p = {1}", x, p); } return ret; } }; // Try to bracket root, test domain endoints if this fails double lowerBound = getDomainLowerBound(p); double upperBound = getDomainUpperBound(p); double[] bracket = null; try { bracket = UnivariateRealSolverUtils.bracket( rootFindingFunction, getInitialDomain(p), lowerBound, upperBound); } catch (ConvergenceException ex) { /* * Check domain endpoints to see if one gives value that is within * the default solver's defaultAbsoluteAccuracy of 0 (will be the * case if density has bounded support and p is 0 or 1). */ if (Math.abs(rootFindingFunction.value(lowerBound)) < getSolverAbsoluteAccuracy()) { return lowerBound; } if (Math.abs(rootFindingFunction.value(upperBound)) < getSolverAbsoluteAccuracy()) { return upperBound; } // Failed bracket convergence was not because of corner solution throw new MathException(ex); } // find root double eps = 10.0 * getSolverAbsoluteAccuracy(); double root = 0; while (Math.abs(root) < 1000*eps && eps > 1e-320) { eps /= 10.0; root = UnivariateRealSolverUtils.solve(rootFindingFunction, // override getSolverAbsoluteAccuracy() to use a Brent solver with // absolute accuracy different from BrentSolver default bracket[0], bracket[1], eps); } if (Math.abs(root) < eps) { root = 0; } // double root = UnivariateRealSolverUtils.solve(rootFindingFunction, // // override getSolverAbsoluteAccuracy() to use a Brent solver with // // absolute accuracy different from BrentSolver default // bracket[0], bracket[1], getSolverAbsoluteAccuracy()); return root; } /** * Access the initial domain value, based on <code>p</code>, 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 */ protected abstract double getInitialDomain(double p); /** * Access the domain value lower bound, based on <code>p</code>, 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 < <i>lower bound</i>) < <code>p</code> */ protected abstract double getDomainLowerBound(double p); /** * Access the domain value upper bound, based on <code>p</code>, 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 < <i>upper bound</i>) > <code>p</code> */ protected abstract double getDomainUpperBound(double p); /** * Returns the solver absolute accuracy for inverse cum computation. * * @return the maximum absolute error in inverse cumulative probability estimates * @since 2.1 */ protected double getSolverAbsoluteAccuracy() { return solverAbsoluteAccuracy; } }