001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018package org.apache.commons.math3.distribution;
019
020import org.apache.commons.math3.exception.NumberIsTooLargeException;
021import org.apache.commons.math3.exception.NumberIsTooSmallException;
022import org.apache.commons.math3.exception.OutOfRangeException;
023import org.apache.commons.math3.exception.util.LocalizedFormats;
024import org.apache.commons.math3.util.FastMath;
025import org.apache.commons.math3.random.RandomGenerator;
026import org.apache.commons.math3.random.Well19937c;
027
028/**
029 * Implementation of the triangular real distribution.
030 *
031 * @see <a href="http://en.wikipedia.org/wiki/Triangular_distribution">
032 * Triangular distribution (Wikipedia)</a>
033 *
034 * @version $Id: TriangularDistribution.java 1416643 2012-12-03 19:37:14Z tn $
035 * @since 3.0
036 */
037public class TriangularDistribution extends AbstractRealDistribution {
038    /** Serializable version identifier. */
039    private static final long serialVersionUID = 20120112L;
040    /** Lower limit of this distribution (inclusive). */
041    private final double a;
042    /** Upper limit of this distribution (inclusive). */
043    private final double b;
044    /** Mode of this distribution. */
045    private final double c;
046    /** Inverse cumulative probability accuracy. */
047    private final double solverAbsoluteAccuracy;
048
049    /**
050     * Creates a triangular real distribution using the given lower limit,
051     * upper limit, and mode.
052     *
053     * @param a Lower limit of this distribution (inclusive).
054     * @param b Upper limit of this distribution (inclusive).
055     * @param c Mode of this distribution.
056     * @throws NumberIsTooLargeException if {@code a >= b} or if {@code c > b}.
057     * @throws NumberIsTooSmallException if {@code c < a}.
058     */
059    public TriangularDistribution(double a, double c, double b)
060        throws NumberIsTooLargeException, NumberIsTooSmallException {
061        this(new Well19937c(), a, c, b);
062    }
063
064    /**
065     * Creates a triangular distribution.
066     *
067     * @param rng Random number generator.
068     * @param a Lower limit of this distribution (inclusive).
069     * @param b Upper limit of this distribution (inclusive).
070     * @param c Mode of this distribution.
071     * @throws NumberIsTooLargeException if {@code a >= b} or if {@code c > b}.
072     * @throws NumberIsTooSmallException if {@code c < a}.
073     * @since 3.1
074     */
075    public TriangularDistribution(RandomGenerator rng,
076                                  double a,
077                                  double c,
078                                  double b)
079        throws NumberIsTooLargeException, NumberIsTooSmallException {
080        super(rng);
081
082        if (a >= b) {
083            throw new NumberIsTooLargeException(
084                            LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND,
085                            a, b, false);
086        }
087        if (c < a) {
088            throw new NumberIsTooSmallException(
089                    LocalizedFormats.NUMBER_TOO_SMALL, c, a, true);
090        }
091        if (c > b) {
092            throw new NumberIsTooLargeException(
093                    LocalizedFormats.NUMBER_TOO_LARGE, c, b, true);
094        }
095
096        this.a = a;
097        this.c = c;
098        this.b = b;
099        solverAbsoluteAccuracy = FastMath.max(FastMath.ulp(a), FastMath.ulp(b));
100    }
101
102    /**
103     * Returns the mode {@code c} of this distribution.
104     *
105     * @return the mode {@code c} of this distribution
106     */
107    public double getMode() {
108        return c;
109    }
110
111    /**
112     * {@inheritDoc}
113     *
114     * <p>
115     * For this distribution, the returned value is not really meaningful,
116     * since exact formulas are implemented for the computation of the
117     * {@link #inverseCumulativeProbability(double)} (no solver is invoked).
118     * </p>
119     * <p>
120     * For lower limit {@code a} and upper limit {@code b}, the current
121     * implementation returns {@code max(ulp(a), ulp(b)}.
122     * </p>
123     */
124    @Override
125    protected double getSolverAbsoluteAccuracy() {
126        return solverAbsoluteAccuracy;
127    }
128
129    /**
130     * {@inheritDoc}
131     *
132     * For lower limit {@code a}, upper limit {@code b} and mode {@code c}, the
133     * PDF is given by
134     * <ul>
135     * <li>{@code 2 * (x - a) / [(b - a) * (c - a)]} if {@code a <= x < c},</li>
136     * <li>{@code 2 / (b - a)} if {@code x = c},</li>
137     * <li>{@code 2 * (b - x) / [(b - a) * (b - c)]} if {@code c < x <= b},</li>
138     * <li>{@code 0} otherwise.
139     * </ul>
140     */
141    public double density(double x) {
142        if (x < a) {
143            return 0;
144        }
145        if (a <= x && x < c) {
146            double divident = 2 * (x - a);
147            double divisor = (b - a) * (c - a);
148            return divident / divisor;
149        }
150        if (x == c) {
151            return 2 / (b - a);
152        }
153        if (c < x && x <= b) {
154            double divident = 2 * (b - x);
155            double divisor = (b - a) * (b - c);
156            return divident / divisor;
157        }
158        return 0;
159    }
160
161    /**
162     * {@inheritDoc}
163     *
164     * For lower limit {@code a}, upper limit {@code b} and mode {@code c}, the
165     * CDF is given by
166     * <ul>
167     * <li>{@code 0} if {@code x < a},</li>
168     * <li>{@code (x - a)^2 / [(b - a) * (c - a)]} if {@code a <= x < c},</li>
169     * <li>{@code (c - a) / (b - a)} if {@code x = c},</li>
170     * <li>{@code 1 - (b - x)^2 / [(b - a) * (b - c)]} if {@code c < x <= b},</li>
171     * <li>{@code 1} if {@code x > b}.</li>
172     * </ul>
173     */
174    public double cumulativeProbability(double x)  {
175        if (x < a) {
176            return 0;
177        }
178        if (a <= x && x < c) {
179            double divident = (x - a) * (x - a);
180            double divisor = (b - a) * (c - a);
181            return divident / divisor;
182        }
183        if (x == c) {
184            return (c - a) / (b - a);
185        }
186        if (c < x && x <= b) {
187            double divident = (b - x) * (b - x);
188            double divisor = (b - a) * (b - c);
189            return 1 - (divident / divisor);
190        }
191        return 1;
192    }
193
194    /**
195     * {@inheritDoc}
196     *
197     * For lower limit {@code a}, upper limit {@code b}, and mode {@code c},
198     * the mean is {@code (a + b + c) / 3}.
199     */
200    public double getNumericalMean() {
201        return (a + b + c) / 3;
202    }
203
204    /**
205     * {@inheritDoc}
206     *
207     * For lower limit {@code a}, upper limit {@code b}, and mode {@code c},
208     * the variance is {@code (a^2 + b^2 + c^2 - a * b - a * c - b * c) / 18}.
209     */
210    public double getNumericalVariance() {
211        return (a * a + b * b + c * c - a * b - a * c - b * c) / 18;
212    }
213
214    /**
215     * {@inheritDoc}
216     *
217     * The lower bound of the support is equal to the lower limit parameter
218     * {@code a} of the distribution.
219     *
220     * @return lower bound of the support
221     */
222    public double getSupportLowerBound() {
223        return a;
224    }
225
226    /**
227     * {@inheritDoc}
228     *
229     * The upper bound of the support is equal to the upper limit parameter
230     * {@code b} of the distribution.
231     *
232     * @return upper bound of the support
233     */
234    public double getSupportUpperBound() {
235        return b;
236    }
237
238    /** {@inheritDoc} */
239    public boolean isSupportLowerBoundInclusive() {
240        return true;
241    }
242
243    /** {@inheritDoc} */
244    public boolean isSupportUpperBoundInclusive() {
245        return true;
246    }
247
248    /**
249     * {@inheritDoc}
250     *
251     * The support of this distribution is connected.
252     *
253     * @return {@code true}
254     */
255    public boolean isSupportConnected() {
256        return true;
257    }
258
259    @Override
260    public double inverseCumulativeProbability(double p)
261        throws OutOfRangeException {
262        if (p < 0 || p > 1) {
263            throw new OutOfRangeException(p, 0, 1);
264        }
265        if (p == 0) {
266            return a;
267        }
268        if (p == 1) {
269            return b;
270        }
271        if (p < (c - a) / (b - a)) {
272            return a + FastMath.sqrt(p * (b - a) * (c - a));
273        }
274        return b - FastMath.sqrt((1 - p) * (b - a) * (b - c));
275    }
276}