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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.math.distribution; import java.io.Serializable; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.exception.util.LocalizedFormats; import org.apache.commons.math.special.Gamma; import org.apache.commons.math.util.FastMath; /** * Default implementation of * {@link org.apache.commons.math.distribution.WeibullDistribution}. * * @since 1.1 * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ */ public class WeibullDistributionImpl extends AbstractContinuousDistribution implements WeibullDistribution, 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 = 8589540077390120676L; /** The shape parameter. */ private double shape; /** The scale parameter. */ private double scale; /** Inverse cumulative probability accuracy */ private final double solverAbsoluteAccuracy; /** Cached numerical mean */ private double numericalMean = Double.NaN; /** Whether or not the numerical mean has been calculated */ private boolean numericalMeanIsCalculated = false; /** Cached numerical variance */ private double numericalVariance = Double.NaN; /** Whether or not the numerical variance has been calculated */ private boolean numericalVarianceIsCalculated = false; /** * Creates weibull distribution with the given shape and scale and a * location equal to zero. * @param alpha the shape parameter. * @param beta the scale parameter. */ public WeibullDistributionImpl(double alpha, double beta) { this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY); } /** * Creates weibull distribution with the given shape, scale and inverse * cumulative probability accuracy and a location equal to zero. * @param alpha the shape parameter. * @param beta the scale parameter. * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}) * @since 2.1 */ public WeibullDistributionImpl(double alpha, double beta, double inverseCumAccuracy) { super(); setShapeInternal(alpha); setScaleInternal(beta); solverAbsoluteAccuracy = inverseCumAccuracy; } /** * For this distribution, X, this method returns P(X < <code>x</code>). * @param x the value at which the CDF is evaluated. * @return CDF evaluated at <code>x</code>. */ public double cumulativeProbability(double x) { double ret; if (x <= 0.0) { ret = 0.0; } else { ret = 1.0 - FastMath.exp(-FastMath.pow(x / scale, shape)); } return ret; } /** * Access the shape parameter. * @return the shape parameter. */ public double getShape() { return shape; } /** * Access the scale parameter. * @return the scale parameter. */ public double getScale() { return scale; } /** * 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) { if (x < 0) { return 0; } final double xscale = x / scale; final double xscalepow = FastMath.pow(xscale, shape - 1); /* * FastMath.pow(x / scale, shape) = * FastMath.pow(xscale, shape) = * FastMath.pow(xscale, shape - 1) * xscale */ final double xscalepowshape = xscalepow * xscale; return (shape / scale) * xscalepow * FastMath.exp(-xscalepowshape); } /** * For this distribution, X, this method returns the critical point x, such * that P(X < x) = <code>p</code>. * <p> * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and * <code>Double.POSITIVE_INFINITY</code> for p=1.</p> * * @param p the desired probability * @return x, such that P(X < x) = <code>p</code> * @throws IllegalArgumentException if <code>p</code> is not a valid * probability. */ @Override public double inverseCumulativeProbability(double p) { double ret; if (p < 0.0 || p > 1.0) { throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0); } else if (p == 0) { ret = 0.0; } else if (p == 1) { ret = Double.POSITIVE_INFINITY; } else { ret = scale * FastMath.pow(-FastMath.log(1.0 - p), 1.0 / shape); } return ret; } /** * Modify the shape parameter. * @param alpha the new shape parameter value. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setShape(double alpha) { setShapeInternal(alpha); invalidateParameterDependentMoments(); } /** * Modify the shape parameter. * @param alpha the new shape parameter value. */ private void setShapeInternal(double alpha) { if (alpha <= 0.0) { throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SHAPE, alpha); } this.shape = alpha; } /** * Modify the scale parameter. * @param beta the new scale parameter value. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setScale(double beta) { setScaleInternal(beta); invalidateParameterDependentMoments(); } /** * Modify the scale parameter. * @param beta the new scale parameter value. */ private void setScaleInternal(double beta) { if (beta <= 0.0) { throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SCALE, beta); } this.scale = beta; } /** * 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> */ @Override protected double getDomainLowerBound(double p) { return 0.0; } /** * 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> */ @Override protected double getDomainUpperBound(double p) { return Double.MAX_VALUE; } /** * 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 */ @Override protected double getInitialDomain(double p) { // use median return FastMath.pow(scale * FastMath.log(2.0), 1.0 / shape); } /** * 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 no matter 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 * no matter the parameters. * * @return upper bound of the support (always Double.POSITIVE_INFINITY) * @since 2.2 */ public double getSupportUpperBound() { return Double.POSITIVE_INFINITY; } /** * Calculates the mean. * * The mean is <code>scale * Gamma(1 + (1 / shape))</code> * where <code>Gamma(...)</code> is the Gamma-function * * @return the mean * @since 2.2 */ protected double calculateNumericalMean() { final double sh = getShape(); final double sc = getScale(); return sc * FastMath.exp(Gamma.logGamma(1 + (1 / sh))); } /** * Calculates the variance. * * The variance is * <code>scale^2 * Gamma(1 + (2 / shape)) - mean^2</code> * where <code>Gamma(...)</code> is the Gamma-function * * @return the variance * @since 2.2 */ private double calculateNumericalVariance() { final double sh = getShape(); final double sc = getScale(); final double mn = getNumericalMean(); return (sc * sc) * FastMath.exp(Gamma.logGamma(1 + (2 / sh))) - (mn * mn); } /** * Returns the mean of the distribution. * * @return the mean or Double.NaN if it's not defined * @since 2.2 */ public double getNumericalMean() { if (!numericalMeanIsCalculated) { numericalMean = calculateNumericalMean(); numericalMeanIsCalculated = true; } return numericalMean; } /** * Returns the variance of the distribution. * * @return the variance (possibly Double.POSITIVE_INFINITY as * for certain cases in {@link TDistributionImpl}) or * Double.NaN if it's not defined * @since 2.2 */ public double getNumericalVariance() { if (!numericalVarianceIsCalculated) { numericalVariance = calculateNumericalVariance(); numericalVarianceIsCalculated = true; } return numericalVariance; } /** * Invalidates the cached mean and variance. */ private void invalidateParameterDependentMoments() { numericalMeanIsCalculated = false; numericalVarianceIsCalculated = false; } }