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 */ 017 018 package org.apache.commons.math3.distribution; 019 020 import org.apache.commons.math3.exception.NumberIsTooLargeException; 021 import org.apache.commons.math3.exception.NumberIsTooSmallException; 022 import org.apache.commons.math3.exception.OutOfRangeException; 023 import org.apache.commons.math3.exception.util.LocalizedFormats; 024 import org.apache.commons.math3.util.FastMath; 025 import org.apache.commons.math3.random.RandomGenerator; 026 import 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 */ 037 public 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 }