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Statistical sampling library for use in virtdata libraries, based
on apache commons math 4
/*
* 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.statistics.distribution;
import org.apache.commons.numbers.gamma.LogGamma;
/**
* Implementation of the Weibull distribution. This implementation uses the
* two parameter form of the distribution defined by
*
* Weibull Distribution, equations (1) and (2).
*
* @see Weibull distribution (Wikipedia)
* @see Weibull distribution (MathWorld)
*
* @since 1.1
*/
public class WeibullDistribution extends AbstractContinuousDistribution {
/** The shape parameter. */
private final double shape;
/** The scale parameter. */
private final double scale;
/**
* Creates a distribution.
*
* @param alpha Shape parameter.
* @param beta Scale parameter.
* @throws IllegalArgumentException if {@code alpha <= 0} or {@code beta <= 0}.
*/
public WeibullDistribution(double alpha,
double beta) {
if (alpha <= 0) {
throw new DistributionException(DistributionException.NEGATIVE,
alpha);
}
if (beta <= 0) {
throw new DistributionException(DistributionException.NEGATIVE,
beta);
}
scale = beta;
shape = alpha;
}
/**
* 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} */
@Override
public double density(double x) {
if (x < 0) {
return 0;
}
final double xscale = x / scale;
final double xscalepow = Math.pow(xscale, shape - 1);
/*
* Math.pow(x / scale, shape) =
* Math.pow(xscale, shape) =
* Math.pow(xscale, shape - 1) * xscale
*/
final double xscalepowshape = xscalepow * xscale;
return (shape / scale) * xscalepow * Math.exp(-xscalepowshape);
}
/** {@inheritDoc} */
@Override
public double logDensity(double x) {
if (x < 0) {
return Double.NEGATIVE_INFINITY;
}
final double xscale = x / scale;
final double logxscalepow = Math.log(xscale) * (shape - 1);
/*
* Math.pow(x / scale, shape) =
* Math.pow(xscale, shape) =
* Math.pow(xscale, shape - 1) * xscale
*/
final double xscalepowshape = Math.exp(logxscalepow) * xscale;
return Math.log(shape / scale) + logxscalepow - xscalepowshape;
}
/** {@inheritDoc} */
@Override
public double cumulativeProbability(double x) {
double ret;
if (x <= 0.0) {
ret = 0.0;
} else {
ret = 1.0 - Math.exp(-Math.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 ||
p > 1) {
throw new DistributionException(DistributionException.OUT_OF_RANGE, p, 0, 1);
} else if (p == 0) {
ret = 0.0;
} else if (p == 1) {
ret = Double.POSITIVE_INFINITY;
} else {
ret = scale * Math.pow(-Math.log1p(-p), 1.0 / shape);
}
return ret;
}
/**
* {@inheritDoc}
*
* The mean is {@code scale * Gamma(1 + (1 / shape))}, where {@code Gamma()}
* is the Gamma-function.
*/
@Override
public double getMean() {
final double sh = getShape();
final double sc = getScale();
return sc * Math.exp(LogGamma.value(1 + (1 / sh)));
}
/**
* {@inheritDoc}
*
* The variance is {@code scale^2 * Gamma(1 + (2 / shape)) - mean^2}
* where {@code Gamma()} is the Gamma-function.
*/
@Override
public double getVariance() {
final double sh = getShape();
final double sc = getScale();
final double mn = getMean();
return (sc * sc) * Math.exp(LogGamma.value(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)
*/
@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
* {@code Double.POSITIVE_INFINITY})
*/
@Override
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
@Override
public boolean isSupportConnected() {
return true;
}
}