/*
* 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.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.special.Gamma;
import org.apache.commons.math3.util.FastMath;
/**
* Implementation of the Weibull distribution. This implementation uses the
* two parameter form of the distribution defined by
* <a href="http://mathworld.wolfram.com/WeibullDistribution.html">
* Weibull Distribution</a>, equations (1) and (2).
*
* @see <a href="http://en.wikipedia.org/wiki/Weibull_distribution">Weibull distribution (Wikipedia)</a>
* @see <a href="http://mathworld.wolfram.com/WeibullDistribution.html">Weibull distribution (MathWorld)</a>
* @since 1.1 (changed to concrete class in 3.0)
*/
public class WeibullDistribution 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 = 8589540077390120676L;
/** The shape parameter. */
private final double shape;
/** The scale parameter. */
private final 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;
/**
* Create a Weibull distribution with the given shape and scale and a
* location equal to zero.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param alpha Shape parameter.
* @param beta Scale parameter.
* @throws NotStrictlyPositiveException if {@code alpha <= 0} or
* {@code beta <= 0}.
*/
public WeibullDistribution(double alpha, double beta)
throws NotStrictlyPositiveException {
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.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @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 WeibullDistribution(double alpha, double beta,
double inverseCumAccuracy) {
this(new Well19937c(), alpha, beta, inverseCumAccuracy);
}
/**
* Creates a Weibull distribution.
*
* @param rng Random number generator.
* @param alpha Shape parameter.
* @param beta Scale parameter.
* @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
* @since 3.3
*/
public WeibullDistribution(RandomGenerator rng, double alpha, double beta)
throws NotStrictlyPositiveException {
this(rng, alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates a Weibull distribution.
*
* @param rng Random number generator.
* @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 3.1
*/
public WeibullDistribution(RandomGenerator rng,
double alpha,
double beta,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (alpha <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE,
alpha);
}
if (beta <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.SCALE,
beta);
}
scale = beta;
shape = alpha;
solverAbsoluteAccuracy = inverseCumAccuracy;
}
/**
* Access the shape parameter, {@code alpha}.
*
* @return the shape parameter, {@code alpha}.
*/
public double getShape() {
return shape;
}
/**
* Access the scale parameter, {@code beta}.
*
* @return the scale parameter, {@code beta}.
*/
public double getScale() {
return scale;
}
/** {@inheritDoc} */
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);
}
/** {@inheritDoc} */
@Override
public double logDensity(double x) {
if (x < 0) {
return Double.NEGATIVE_INFINITY;
}
final double xscale = x / scale;
final double logxscalepow = FastMath.log(xscale) * (shape - 1);
/*
* FastMath.pow(x / scale, shape) =
* FastMath.pow(xscale, shape) =
* FastMath.pow(xscale, shape - 1) * xscale
*/
final double xscalepowshape = FastMath.exp(logxscalepow) * xscale;
return FastMath.log(shape / scale) + logxscalepow - xscalepowshape;
}
/** {@inheritDoc} */
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}
*
* Returns {@code 0} when {@code p == 0} and
* {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
*/
@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.log1p(-p), 1.0 / shape);
}
return ret;
}
/**
* 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 mean is {@code scale * Gamma(1 + (1 / shape))}, where {@code Gamma()}
* is the Gamma-function.
*/
public double getNumericalMean() {
if (!numericalMeanIsCalculated) {
numericalMean = calculateNumericalMean();
numericalMeanIsCalculated = true;
}
return numericalMean;
}
/**
* used by {@link #getNumericalMean()}
*
* @return the mean of this distribution
*/
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}
* where {@code Gamma()} is the Gamma-function.
*/
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 sh = getShape();
final double sc = getScale();
final double mn = getNumericalMean();
return (sc * sc) * FastMath.exp(Gamma.logGamma(1 + (2 / sh))) -
(mn * mn);
}
/**
* {@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
* {@code Double.POSITIVE_INFINITY})
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return true;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}