mirror of https://github.com/jlizier/jidt
358 lines
13 KiB
Java
358 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.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.Beta;
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import infodynamics.utils.commonsmath3.util.FastMath;
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/**
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* Implementation of the F-distribution.
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*
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* @see <a href="http://en.wikipedia.org/wiki/F-distribution">F-distribution (Wikipedia)</a>
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* @see <a href="http://mathworld.wolfram.com/F-Distribution.html">F-distribution (MathWorld)</a>
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*/
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public class FDistribution 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 = -8516354193418641566L;
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/** The numerator degrees of freedom. */
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private final double numeratorDegreesOfFreedom;
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/** The numerator degrees of freedom. */
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private final double denominatorDegreesOfFreedom;
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/** Inverse cumulative probability accuracy. */
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private final double solverAbsoluteAccuracy;
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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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* Creates an F distribution using the given degrees of freedom.
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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 numeratorDegreesOfFreedom Numerator degrees of freedom.
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* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
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* @throws NotStrictlyPositiveException if
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* {@code numeratorDegreesOfFreedom <= 0} or
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* {@code denominatorDegreesOfFreedom <= 0}.
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*/
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public FDistribution(double numeratorDegreesOfFreedom,
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double denominatorDegreesOfFreedom)
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throws NotStrictlyPositiveException {
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this(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom,
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DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
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}
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/**
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* Creates an F distribution using the given degrees of freedom
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* and inverse cumulative probability accuracy.
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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 numeratorDegreesOfFreedom Numerator degrees of freedom.
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* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
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* @param inverseCumAccuracy the maximum absolute error in inverse
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* cumulative probability estimates.
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* @throws NotStrictlyPositiveException if
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* {@code numeratorDegreesOfFreedom <= 0} or
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* {@code denominatorDegreesOfFreedom <= 0}.
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* @since 2.1
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*/
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public FDistribution(double numeratorDegreesOfFreedom,
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double denominatorDegreesOfFreedom,
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double inverseCumAccuracy)
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throws NotStrictlyPositiveException {
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this(new Well19937c(), numeratorDegreesOfFreedom,
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denominatorDegreesOfFreedom, inverseCumAccuracy);
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}
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/**
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* Creates an F distribution.
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*
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* @param rng Random number generator.
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* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
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* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
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* @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0} or
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* {@code denominatorDegreesOfFreedom <= 0}.
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* @since 3.3
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*/
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public FDistribution(RandomGenerator rng,
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double numeratorDegreesOfFreedom,
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double denominatorDegreesOfFreedom)
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throws NotStrictlyPositiveException {
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this(rng, numeratorDegreesOfFreedom, denominatorDegreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
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}
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/**
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* Creates an F distribution.
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*
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* @param rng Random number generator.
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* @param numeratorDegreesOfFreedom Numerator degrees of freedom.
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* @param denominatorDegreesOfFreedom Denominator degrees of freedom.
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* @param inverseCumAccuracy the maximum absolute error in inverse
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* cumulative probability estimates.
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* @throws NotStrictlyPositiveException if {@code numeratorDegreesOfFreedom <= 0} or
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* {@code denominatorDegreesOfFreedom <= 0}.
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* @since 3.1
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*/
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public FDistribution(RandomGenerator rng,
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double numeratorDegreesOfFreedom,
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double denominatorDegreesOfFreedom,
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double inverseCumAccuracy)
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throws NotStrictlyPositiveException {
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super(rng);
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if (numeratorDegreesOfFreedom <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
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numeratorDegreesOfFreedom);
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}
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if (denominatorDegreesOfFreedom <= 0) {
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throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
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denominatorDegreesOfFreedom);
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}
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this.numeratorDegreesOfFreedom = numeratorDegreesOfFreedom;
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this.denominatorDegreesOfFreedom = denominatorDegreesOfFreedom;
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solverAbsoluteAccuracy = inverseCumAccuracy;
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}
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/**
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* {@inheritDoc}
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*
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* @since 2.1
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*/
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public double density(double x) {
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return FastMath.exp(logDensity(x));
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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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final double nhalf = numeratorDegreesOfFreedom / 2;
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final double mhalf = denominatorDegreesOfFreedom / 2;
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final double logx = FastMath.log(x);
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final double logn = FastMath.log(numeratorDegreesOfFreedom);
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final double logm = FastMath.log(denominatorDegreesOfFreedom);
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final double lognxm = FastMath.log(numeratorDegreesOfFreedom * x +
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denominatorDegreesOfFreedom);
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return nhalf * logn + nhalf * logx - logx +
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mhalf * logm - nhalf * lognxm - mhalf * lognxm -
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Beta.logBeta(nhalf, mhalf);
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}
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/**
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* {@inheritDoc}
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*
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* The implementation of this method is based on
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* <ul>
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* <li>
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* <a href="http://mathworld.wolfram.com/F-Distribution.html">
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* F-Distribution</a>, equation (4).
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* </li>
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* </ul>
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*/
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public double cumulativeProbability(double x) {
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double ret;
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if (x <= 0) {
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ret = 0;
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} else {
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double n = numeratorDegreesOfFreedom;
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double m = denominatorDegreesOfFreedom;
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ret = Beta.regularizedBeta((n * x) / (m + n * x),
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0.5 * n,
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0.5 * m);
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}
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return ret;
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}
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/**
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* Access the numerator degrees of freedom.
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*
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* @return the numerator degrees of freedom.
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*/
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public double getNumeratorDegreesOfFreedom() {
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return numeratorDegreesOfFreedom;
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}
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/**
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* Access the denominator degrees of freedom.
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*
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* @return the denominator degrees of freedom.
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*/
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public double getDenominatorDegreesOfFreedom() {
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return denominatorDegreesOfFreedom;
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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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* For denominator degrees of freedom parameter {@code b}, the mean is
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* <ul>
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* <li>if {@code b > 2} then {@code b / (b - 2)},</li>
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* <li>else undefined ({@code Double.NaN}).
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* </ul>
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*/
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public double getNumericalMean() {
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final double denominatorDF = getDenominatorDegreesOfFreedom();
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if (denominatorDF > 2) {
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return denominatorDF / (denominatorDF - 2);
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}
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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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* For numerator degrees of freedom parameter {@code a} and denominator
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* degrees of freedom parameter {@code b}, the variance is
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* <ul>
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* <li>
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* if {@code b > 4} then
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* {@code [2 * b^2 * (a + b - 2)] / [a * (b - 2)^2 * (b - 4)]},
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* </li>
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* <li>else undefined ({@code Double.NaN}).
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* </ul>
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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 denominatorDF = getDenominatorDegreesOfFreedom();
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if (denominatorDF > 4) {
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final double numeratorDF = getNumeratorDegreesOfFreedom();
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final double denomDFMinusTwo = denominatorDF - 2;
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return ( 2 * (denominatorDF * denominatorDF) * (numeratorDF + denominatorDF - 2) ) /
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( (numeratorDF * (denomDFMinusTwo * denomDFMinusTwo) * (denominatorDF - 4)) );
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}
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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 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 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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