mirror of https://github.com/jlizier/jidt
286 lines
9.6 KiB
Java
286 lines
9.6 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.util.FastMath;
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/**
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* Implementation of the Cauchy distribution.
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*
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* @see <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution (Wikipedia)</a>
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* @see <a href="http://mathworld.wolfram.com/CauchyDistribution.html">Cauchy 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 CauchyDistribution 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 median of this distribution. */
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private final double median;
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/** The scale of this distribution. */
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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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/**
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* Creates a Cauchy distribution with the median equal to zero and scale
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* equal to one.
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*/
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public CauchyDistribution() {
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this(0, 1);
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}
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/**
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* Creates a Cauchy distribution using the given median and scale.
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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 median Median for this distribution.
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* @param scale Scale parameter for this distribution.
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*/
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public CauchyDistribution(double median, double scale) {
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this(median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
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}
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/**
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* Creates a Cauchy distribution using the given median and scale.
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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 median Median for this distribution.
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* @param scale Scale parameter for this distribution.
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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 scale <= 0}.
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* @since 2.1
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*/
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public CauchyDistribution(double median, double scale,
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double inverseCumAccuracy) {
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this(new Well19937c(), median, scale, inverseCumAccuracy);
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}
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/**
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* Creates a Cauchy distribution.
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*
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* @param rng Random number generator.
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* @param median Median for this distribution.
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* @param scale Scale parameter for this distribution.
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* @throws NotStrictlyPositiveException if {@code scale <= 0}.
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* @since 3.3
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*/
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public CauchyDistribution(RandomGenerator rng, double median, double scale) {
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this(rng, median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
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}
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/**
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* Creates a Cauchy distribution.
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*
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* @param rng Random number generator.
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* @param median Median for this distribution.
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* @param scale Scale parameter for this distribution.
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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 scale <= 0}.
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* @since 3.1
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*/
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public CauchyDistribution(RandomGenerator rng,
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double median,
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double scale,
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double inverseCumAccuracy) {
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super(rng);
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if (scale <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
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}
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this.scale = scale;
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this.median = median;
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solverAbsoluteAccuracy = inverseCumAccuracy;
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}
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/** {@inheritDoc} */
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public double cumulativeProbability(double x) {
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return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
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}
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/**
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* Access the median.
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*
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* @return the median for this distribution.
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*/
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public double getMedian() {
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return median;
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}
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/**
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* Access the scale parameter.
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*
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* @return the scale parameter for this distribution.
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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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final double dev = x - median;
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return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
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}
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/**
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* {@inheritDoc}
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*
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* Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0}
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* and {@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) throws OutOfRangeException {
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double ret;
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if (p < 0 || p > 1) {
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throw new OutOfRangeException(p, 0, 1);
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} else if (p == 0) {
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ret = Double.NEGATIVE_INFINITY;
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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 = median + scale * FastMath.tan(FastMath.PI * (p - .5));
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}
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return ret;
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}
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/** {@inheritDoc} */
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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 always undefined no matter the parameters.
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*
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* @return mean (always Double.NaN)
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*/
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public double getNumericalMean() {
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return Double.NaN;
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}
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/**
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* {@inheritDoc}
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*
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* The variance is always undefined no matter the parameters.
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*
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* @return variance (always Double.NaN)
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*/
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public double getNumericalVariance() {
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return Double.NaN;
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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 negative infinity no matter
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* the parameters.
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*
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* @return lower bound of the support (always Double.NEGATIVE_INFINITY)
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*/
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public double getSupportLowerBound() {
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return Double.NEGATIVE_INFINITY;
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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 no matter
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* the parameters.
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*
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* @return upper bound of the support (always 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 false;
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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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