mirror of https://github.com/jlizier/jidt
383 lines
13 KiB
Java
383 lines
13 KiB
Java
/*
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* Java Information Dynamics Toolkit (JIDT)
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* Copyright (C) 2017, Joseph T. Lizier
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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/*
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* This class was originally distributed as part of the Apache Commons
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* Math3 library (3.6.1), under the Apache License Version 2.0, which is
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* copied below. This Apache 2 software is now included as a derivative
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* work in the GPLv3 licensed JIDT project, as per:
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* http://www.apache.org/licenses/GPL-compatibility.html
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*
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* The original Apache source code has been modified as follows:
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* -- We have modified package names to sit inside the JIDT structure.
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*/
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package infodynamics.utils.commonsmath3.distribution;
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import infodynamics.utils.commonsmath3.exception.NotStrictlyPositiveException;
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import infodynamics.utils.commonsmath3.exception.OutOfRangeException;
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import infodynamics.utils.commonsmath3.exception.util.LocalizedFormats;
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import infodynamics.utils.commonsmath3.random.RandomGenerator;
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import infodynamics.utils.commonsmath3.random.Well19937c;
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import infodynamics.utils.commonsmath3.special.Gamma;
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import infodynamics.utils.commonsmath3.util.FastMath;
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/**
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* Implementation of the Weibull distribution. This implementation uses the
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* two parameter form of the distribution defined by
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* <a href="http://mathworld.wolfram.com/WeibullDistribution.html">
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* Weibull Distribution</a>, equations (1) and (2).
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*
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* @see <a href="http://en.wikipedia.org/wiki/Weibull_distribution">Weibull distribution (Wikipedia)</a>
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* @see <a href="http://mathworld.wolfram.com/WeibullDistribution.html">Weibull distribution (MathWorld)</a>
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* @since 1.1 (changed to concrete class in 3.0)
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*/
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public class WeibullDistribution extends AbstractRealDistribution {
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/**
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* Default inverse cumulative probability accuracy.
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* @since 2.1
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*/
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public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
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/** Serializable version identifier. */
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private static final long serialVersionUID = 8589540077390120676L;
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/** The shape parameter. */
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private final double shape;
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/** The scale parameter. */
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private final double scale;
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/** Inverse cumulative probability accuracy. */
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private final double solverAbsoluteAccuracy;
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/** Cached numerical mean */
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private double numericalMean = Double.NaN;
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/** Whether or not the numerical mean has been calculated */
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private boolean numericalMeanIsCalculated = false;
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/** Cached numerical variance */
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private double numericalVariance = Double.NaN;
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/** Whether or not the numerical variance has been calculated */
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private boolean numericalVarianceIsCalculated = false;
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/**
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* Create a Weibull distribution with the given shape and scale and a
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* location equal to zero.
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* <p>
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* <b>Note:</b> this constructor will implicitly create an instance of
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* {@link Well19937c} as random generator to be used for sampling only (see
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* {@link #sample()} and {@link #sample(int)}). In case no sampling is
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* needed for the created distribution, it is advised to pass {@code null}
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* as random generator via the appropriate constructors to avoid the
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* additional initialisation overhead.
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*
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* @param alpha Shape parameter.
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* @param beta Scale parameter.
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* @throws NotStrictlyPositiveException if {@code alpha <= 0} or
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* {@code beta <= 0}.
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*/
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public WeibullDistribution(double alpha, double beta)
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throws NotStrictlyPositiveException {
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this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
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}
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/**
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* Create a Weibull distribution with the given shape, scale and inverse
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* cumulative probability accuracy and a location equal to zero.
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* <p>
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* <b>Note:</b> this constructor will implicitly create an instance of
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* {@link Well19937c} as random generator to be used for sampling only (see
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* {@link #sample()} and {@link #sample(int)}). In case no sampling is
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* needed for the created distribution, it is advised to pass {@code null}
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* as random generator via the appropriate constructors to avoid the
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* additional initialisation overhead.
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*
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* @param alpha Shape parameter.
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* @param beta Scale parameter.
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* @param inverseCumAccuracy Maximum absolute error in inverse
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* cumulative probability estimates
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* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
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* @throws NotStrictlyPositiveException if {@code alpha <= 0} or
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* {@code beta <= 0}.
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* @since 2.1
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*/
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public WeibullDistribution(double alpha, double beta,
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double inverseCumAccuracy) {
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this(new Well19937c(), alpha, beta, inverseCumAccuracy);
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}
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/**
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* Creates a Weibull distribution.
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*
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* @param rng Random number generator.
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* @param alpha Shape parameter.
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* @param beta Scale parameter.
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* @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
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* @since 3.3
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*/
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public WeibullDistribution(RandomGenerator rng, double alpha, double beta)
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throws NotStrictlyPositiveException {
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this(rng, alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
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}
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/**
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* Creates a Weibull distribution.
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*
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* @param rng Random number generator.
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* @param alpha Shape parameter.
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* @param beta Scale parameter.
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* @param inverseCumAccuracy Maximum absolute error in inverse
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* cumulative probability estimates
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* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
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* @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
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* @since 3.1
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*/
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public WeibullDistribution(RandomGenerator rng,
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double alpha,
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double beta,
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double inverseCumAccuracy)
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throws NotStrictlyPositiveException {
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super(rng);
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if (alpha <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE,
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alpha);
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}
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if (beta <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.SCALE,
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beta);
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}
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scale = beta;
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shape = alpha;
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solverAbsoluteAccuracy = inverseCumAccuracy;
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}
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/**
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* Access the shape parameter, {@code alpha}.
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*
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* @return the shape parameter, {@code alpha}.
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*/
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public double getShape() {
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return shape;
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}
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/**
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* Access the scale parameter, {@code beta}.
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*
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* @return the scale parameter, {@code beta}.
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*/
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public double getScale() {
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return scale;
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}
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/** {@inheritDoc} */
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public double density(double x) {
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if (x < 0) {
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return 0;
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}
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final double xscale = x / scale;
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final double xscalepow = FastMath.pow(xscale, shape - 1);
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/*
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* FastMath.pow(x / scale, shape) =
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* FastMath.pow(xscale, shape) =
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* FastMath.pow(xscale, shape - 1) * xscale
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*/
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final double xscalepowshape = xscalepow * xscale;
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return (shape / scale) * xscalepow * FastMath.exp(-xscalepowshape);
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}
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/** {@inheritDoc} */
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@Override
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public double logDensity(double x) {
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if (x < 0) {
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return Double.NEGATIVE_INFINITY;
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}
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final double xscale = x / scale;
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final double logxscalepow = FastMath.log(xscale) * (shape - 1);
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/*
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* FastMath.pow(x / scale, shape) =
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* FastMath.pow(xscale, shape) =
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* FastMath.pow(xscale, shape - 1) * xscale
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*/
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final double xscalepowshape = FastMath.exp(logxscalepow) * xscale;
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return FastMath.log(shape / scale) + logxscalepow - xscalepowshape;
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}
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/** {@inheritDoc} */
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public double cumulativeProbability(double x) {
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double ret;
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if (x <= 0.0) {
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ret = 0.0;
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} else {
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ret = 1.0 - FastMath.exp(-FastMath.pow(x / scale, shape));
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}
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return ret;
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}
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/**
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* {@inheritDoc}
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*
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* Returns {@code 0} when {@code p == 0} and
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* {@code Double.POSITIVE_INFINITY} when {@code p == 1}.
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*/
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@Override
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public double inverseCumulativeProbability(double p) {
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double ret;
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if (p < 0.0 || p > 1.0) {
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throw new OutOfRangeException(p, 0.0, 1.0);
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} else if (p == 0) {
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ret = 0.0;
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} else if (p == 1) {
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ret = Double.POSITIVE_INFINITY;
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} else {
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ret = scale * FastMath.pow(-FastMath.log1p(-p), 1.0 / shape);
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}
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return ret;
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}
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/**
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* Return the absolute accuracy setting of the solver used to estimate
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* inverse cumulative probabilities.
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*
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* @return the solver absolute accuracy.
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* @since 2.1
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*/
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@Override
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protected double getSolverAbsoluteAccuracy() {
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return solverAbsoluteAccuracy;
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}
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/**
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* {@inheritDoc}
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*
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* The mean is {@code scale * Gamma(1 + (1 / shape))}, where {@code Gamma()}
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* is the Gamma-function.
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*/
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public double getNumericalMean() {
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if (!numericalMeanIsCalculated) {
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numericalMean = calculateNumericalMean();
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numericalMeanIsCalculated = true;
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}
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return numericalMean;
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}
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/**
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* used by {@link #getNumericalMean()}
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*
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* @return the mean of this distribution
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*/
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protected double calculateNumericalMean() {
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final double sh = getShape();
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final double sc = getScale();
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return sc * FastMath.exp(Gamma.logGamma(1 + (1 / sh)));
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}
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/**
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* {@inheritDoc}
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*
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* The variance is {@code scale^2 * Gamma(1 + (2 / shape)) - mean^2}
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* where {@code Gamma()} is the Gamma-function.
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*/
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public double getNumericalVariance() {
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if (!numericalVarianceIsCalculated) {
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numericalVariance = calculateNumericalVariance();
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numericalVarianceIsCalculated = true;
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}
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return numericalVariance;
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}
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/**
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* used by {@link #getNumericalVariance()}
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*
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* @return the variance of this distribution
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*/
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protected double calculateNumericalVariance() {
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final double sh = getShape();
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final double sc = getScale();
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final double mn = getNumericalMean();
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return (sc * sc) * FastMath.exp(Gamma.logGamma(1 + (2 / sh))) -
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(mn * mn);
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}
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/**
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* {@inheritDoc}
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*
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* The lower bound of the support is always 0 no matter the parameters.
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*
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* @return lower bound of the support (always 0)
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*/
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public double getSupportLowerBound() {
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return 0;
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}
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/**
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* {@inheritDoc}
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*
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* The upper bound of the support is always positive infinity
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* no matter the parameters.
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*
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* @return upper bound of the support (always
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* {@code Double.POSITIVE_INFINITY})
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*/
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public double getSupportUpperBound() {
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return Double.POSITIVE_INFINITY;
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}
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/** {@inheritDoc} */
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public boolean isSupportLowerBoundInclusive() {
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return true;
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}
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/** {@inheritDoc} */
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public boolean isSupportUpperBoundInclusive() {
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return false;
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}
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/**
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* {@inheritDoc}
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*
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* The support of this distribution is connected.
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*
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* @return {@code true}
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*/
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public boolean isSupportConnected() {
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return true;
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}
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}
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