/*
* 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;
}
}