/*
* 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.exception.OutOfRangeException;
import org.apache.commons.math.exception.NotStrictlyPositiveException;
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 $Id: WeibullDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $
*/
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 final double shape;
/** The scale parameter. */
private final double scale;
/** Inverse cumulative probability accuracy. */
private final double solverAbsoluteAccuracy;
/**
* Create a Weibull distribution with the given shape and scale and a
* location equal to zero.
*
* @param alpha Shape parameter.
* @param beta Scale parameter.
*/
public WeibullDistributionImpl(double alpha, double beta) {
this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a Weibull distribution with the given shape, scale and inverse
* cumulative probability accuracy and a location equal to zero.
*
* @param alpha Shape parameter.
* @param beta Scale parameter.
* @param inverseCumAccuracy Maximum absolute error in inverse
* cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code alpha <= 0} or
* {@code beta <= 0}.
* @since 2.1
*/
public WeibullDistributionImpl(double alpha, double beta,
double inverseCumAccuracy) {
if (alpha <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE,
alpha);
}
if (beta <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE,
beta);
}
scale = beta;
shape = alpha;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* For this distribution, {@code X}, this method returns {@code P(X < x)}.
*
* @param x Value at which the CDF is evaluated.
* @return the CDF evaluated at {@code x}.
*/
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;
}
/**
* {@inheritDoc}
*/
public double getShape() {
return shape;
}
/**
* {@inheritDoc}
*/
public double getScale() {
return scale;
}
/**
* {@inheritDoc}
*/
@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, {@code X}, this method returns the critical
* point {@code x}, such that {@code P(X < x) = p}.
* It will return {@code Double.NEGATIVE_INFINITY} when p = 0 and
* {@code Double.POSITIVE_INFINITY} when p = 1.
*
* @param p Desired probability.
* @return {@code x}, such that {@code P(X < x) = p}.
* @throws OutOfRangeException if {@code p} is not a valid probability.
*/
@Override
public double inverseCumulativeProbability(double p) {
double ret;
if (p < 0.0 || p > 1.0) {
throw new OutOfRangeException(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;
}
/**
* Access the domain value lower bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value lower bound, i.e. {@code P(X < 'lower bound') < p}.
*/
@Override
protected double getDomainLowerBound(double p) {
return 0;
}
/**
* Access the domain value upper bound, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the domain value upper bound, i.e. {@code P(X < 'upper bound') > p}.
*/
@Override
protected double getDomainUpperBound(double p) {
return Double.MAX_VALUE;
}
/**
* Access the initial domain value, based on {@code p}, used to
* bracket a CDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p Desired probability for the critical value.
* @return the 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;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 0 no matter the parameters.
*
* @return lower bound of the support (always 0)
*/
@Override
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)
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* The mean is <code>scale * Gamma(1 + (1 / shape))</code>
* where <code>Gamma(...)</code> is the Gamma-function
*
* @return {@inheritDoc}
*/
@Override
protected double calculateNumericalMean() {
final double sh = getShape();
final double sc = getScale();
return sc * FastMath.exp(Gamma.logGamma(1 + (1 / sh)));
}
/**
* {@inheritDoc}
*
* The variance is
* <code>scale^2 * Gamma(1 + (2 / shape)) - mean^2</code>
* where <code>Gamma(...)</code> is the Gamma-function
*
* @return {@inheritDoc}
*/
@Override
protected 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);
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportLowerBoundInclusive() {
return true;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportUpperBoundInclusive() {
return false;
}
}