Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | package org.apache.commons.math.distribution; |
| 18 | |
| 19 | import java.io.Serializable; |
| 20 | |
| 21 | import org.apache.commons.math.MathException; |
| 22 | import org.apache.commons.math.MathRuntimeException; |
| 23 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 24 | import org.apache.commons.math.special.Beta; |
| 25 | import org.apache.commons.math.util.MathUtils; |
| 26 | import org.apache.commons.math.util.FastMath; |
| 27 | |
| 28 | /** |
| 29 | * The default implementation of {@link PascalDistribution}. |
| 30 | * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $ |
| 31 | * @since 1.2 |
| 32 | */ |
| 33 | public class PascalDistributionImpl extends AbstractIntegerDistribution |
| 34 | implements PascalDistribution, Serializable { |
| 35 | |
| 36 | /** Serializable version identifier */ |
| 37 | private static final long serialVersionUID = 6751309484392813623L; |
| 38 | |
| 39 | /** The number of successes */ |
| 40 | private int numberOfSuccesses; |
| 41 | |
| 42 | /** The probability of success */ |
| 43 | private double probabilityOfSuccess; |
| 44 | |
| 45 | /** |
| 46 | * Create a Pascal distribution with the given number of trials and |
| 47 | * probability of success. |
| 48 | * @param r the number of successes |
| 49 | * @param p the probability of success |
| 50 | */ |
| 51 | public PascalDistributionImpl(int r, double p) { |
| 52 | super(); |
| 53 | setNumberOfSuccessesInternal(r); |
| 54 | setProbabilityOfSuccessInternal(p); |
| 55 | } |
| 56 | |
| 57 | /** |
| 58 | * Access the number of successes for this distribution. |
| 59 | * @return the number of successes |
| 60 | */ |
| 61 | public int getNumberOfSuccesses() { |
| 62 | return numberOfSuccesses; |
| 63 | } |
| 64 | |
| 65 | /** |
| 66 | * Access the probability of success for this distribution. |
| 67 | * @return the probability of success |
| 68 | */ |
| 69 | public double getProbabilityOfSuccess() { |
| 70 | return probabilityOfSuccess; |
| 71 | } |
| 72 | |
| 73 | /** |
| 74 | * Change the number of successes for this distribution. |
| 75 | * @param successes the new number of successes |
| 76 | * @throws IllegalArgumentException if <code>successes</code> is not |
| 77 | * positive. |
| 78 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 79 | */ |
| 80 | @Deprecated |
| 81 | public void setNumberOfSuccesses(int successes) { |
| 82 | setNumberOfSuccessesInternal(successes); |
| 83 | } |
| 84 | |
| 85 | /** |
| 86 | * Change the number of successes for this distribution. |
| 87 | * @param successes the new number of successes |
| 88 | * @throws IllegalArgumentException if <code>successes</code> is not |
| 89 | * positive. |
| 90 | */ |
| 91 | private void setNumberOfSuccessesInternal(int successes) { |
| 92 | if (successes < 0) { |
| 93 | throw MathRuntimeException.createIllegalArgumentException( |
| 94 | LocalizedFormats.NEGATIVE_NUMBER_OF_SUCCESSES, |
| 95 | successes); |
| 96 | } |
| 97 | numberOfSuccesses = successes; |
| 98 | } |
| 99 | |
| 100 | /** |
| 101 | * Change the probability of success for this distribution. |
| 102 | * @param p the new probability of success |
| 103 | * @throws IllegalArgumentException if <code>p</code> is not a valid |
| 104 | * probability. |
| 105 | * @deprecated as of 2.1 (class will become immutable in 3.0) |
| 106 | */ |
| 107 | @Deprecated |
| 108 | public void setProbabilityOfSuccess(double p) { |
| 109 | setProbabilityOfSuccessInternal(p); |
| 110 | } |
| 111 | |
| 112 | /** |
| 113 | * Change the probability of success for this distribution. |
| 114 | * @param p the new probability of success |
| 115 | * @throws IllegalArgumentException if <code>p</code> is not a valid |
| 116 | * probability. |
| 117 | */ |
| 118 | private void setProbabilityOfSuccessInternal(double p) { |
| 119 | if (p < 0.0 || p > 1.0) { |
| 120 | throw MathRuntimeException.createIllegalArgumentException( |
| 121 | LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0); |
| 122 | } |
| 123 | probabilityOfSuccess = p; |
| 124 | } |
| 125 | |
| 126 | /** |
| 127 | * Access the domain value lower bound, based on <code>p</code>, used to |
| 128 | * bracket a PDF root. |
| 129 | * @param p the desired probability for the critical value |
| 130 | * @return domain value lower bound, i.e. P(X < <i>lower bound</i>) < |
| 131 | * <code>p</code> |
| 132 | */ |
| 133 | @Override |
| 134 | protected int getDomainLowerBound(double p) { |
| 135 | return -1; |
| 136 | } |
| 137 | |
| 138 | /** |
| 139 | * Access the domain value upper bound, based on <code>p</code>, used to |
| 140 | * bracket a PDF root. |
| 141 | * @param p the desired probability for the critical value |
| 142 | * @return domain value upper bound, i.e. P(X < <i>upper bound</i>) > |
| 143 | * <code>p</code> |
| 144 | */ |
| 145 | @Override |
| 146 | protected int getDomainUpperBound(double p) { |
| 147 | // use MAX - 1 because MAX causes loop |
| 148 | return Integer.MAX_VALUE - 1; |
| 149 | } |
| 150 | |
| 151 | /** |
| 152 | * For this distribution, X, this method returns P(X ≤ x). |
| 153 | * @param x the value at which the PDF is evaluated |
| 154 | * @return PDF for this distribution |
| 155 | * @throws MathException if the cumulative probability can not be computed |
| 156 | * due to convergence or other numerical errors |
| 157 | */ |
| 158 | @Override |
| 159 | public double cumulativeProbability(int x) throws MathException { |
| 160 | double ret; |
| 161 | if (x < 0) { |
| 162 | ret = 0.0; |
| 163 | } else { |
| 164 | ret = Beta.regularizedBeta(probabilityOfSuccess, |
| 165 | numberOfSuccesses, x + 1); |
| 166 | } |
| 167 | return ret; |
| 168 | } |
| 169 | |
| 170 | /** |
| 171 | * For this distribution, X, this method returns P(X = x). |
| 172 | * @param x the value at which the PMF is evaluated |
| 173 | * @return PMF for this distribution |
| 174 | */ |
| 175 | public double probability(int x) { |
| 176 | double ret; |
| 177 | if (x < 0) { |
| 178 | ret = 0.0; |
| 179 | } else { |
| 180 | ret = MathUtils.binomialCoefficientDouble(x + |
| 181 | numberOfSuccesses - 1, numberOfSuccesses - 1) * |
| 182 | FastMath.pow(probabilityOfSuccess, numberOfSuccesses) * |
| 183 | FastMath.pow(1.0 - probabilityOfSuccess, x); |
| 184 | } |
| 185 | return ret; |
| 186 | } |
| 187 | |
| 188 | /** |
| 189 | * For this distribution, X, this method returns the largest x, such that |
| 190 | * P(X ≤ x) ≤ <code>p</code>. |
| 191 | * <p> |
| 192 | * Returns <code>-1</code> for p=0 and <code>Integer.MAX_VALUE</code> |
| 193 | * for p=1.</p> |
| 194 | * @param p the desired probability |
| 195 | * @return the largest x such that P(X ≤ x) <= p |
| 196 | * @throws MathException if the inverse cumulative probability can not be |
| 197 | * computed due to convergence or other numerical errors. |
| 198 | * @throws IllegalArgumentException if p < 0 or p > 1 |
| 199 | */ |
| 200 | @Override |
| 201 | public int inverseCumulativeProbability(final double p) |
| 202 | throws MathException { |
| 203 | int ret; |
| 204 | |
| 205 | // handle extreme values explicitly |
| 206 | if (p == 0) { |
| 207 | ret = -1; |
| 208 | } else if (p == 1) { |
| 209 | ret = Integer.MAX_VALUE; |
| 210 | } else { |
| 211 | ret = super.inverseCumulativeProbability(p); |
| 212 | } |
| 213 | |
| 214 | return ret; |
| 215 | } |
| 216 | |
| 217 | /** |
| 218 | * Returns the lower bound of the support for the distribution. |
| 219 | * |
| 220 | * The lower bound of the support is always 0 no matter the parameters. |
| 221 | * |
| 222 | * @return lower bound of the support (always 0) |
| 223 | * @since 2.2 |
| 224 | */ |
| 225 | public int getSupportLowerBound() { |
| 226 | return 0; |
| 227 | } |
| 228 | |
| 229 | /** |
| 230 | * Returns the upper bound of the support for the distribution. |
| 231 | * |
| 232 | * The upper bound of the support is always positive infinity |
| 233 | * no matter the parameters. Positive infinity is represented |
| 234 | * by <code>Integer.MAX_VALUE</code> together with |
| 235 | * {@link #isSupportUpperBoundInclusive()} being <code>false</code> |
| 236 | * |
| 237 | * @return upper bound of the support (always <code>Integer.MAX_VALUE</code> for positive infinity) |
| 238 | * @since 2.2 |
| 239 | */ |
| 240 | public int getSupportUpperBound() { |
| 241 | return Integer.MAX_VALUE; |
| 242 | } |
| 243 | |
| 244 | /** |
| 245 | * Returns the mean. |
| 246 | * |
| 247 | * For number of successes <code>r</code> and |
| 248 | * probability of success <code>p</code>, the mean is |
| 249 | * <code>( r * p ) / ( 1 - p )</code> |
| 250 | * |
| 251 | * @return the mean |
| 252 | * @since 2.2 |
| 253 | */ |
| 254 | public double getNumericalMean() { |
| 255 | final double p = getProbabilityOfSuccess(); |
| 256 | final double r = getNumberOfSuccesses(); |
| 257 | return ( r * p ) / ( 1 - p ); |
| 258 | } |
| 259 | |
| 260 | /** |
| 261 | * Returns the variance. |
| 262 | * |
| 263 | * For number of successes <code>r</code> and |
| 264 | * probability of success <code>p</code>, the mean is |
| 265 | * <code>( r * p ) / ( 1 - p )^2</code> |
| 266 | * |
| 267 | * @return the variance |
| 268 | * @since 2.2 |
| 269 | */ |
| 270 | public double getNumericalVariance() { |
| 271 | final double p = getProbabilityOfSuccess(); |
| 272 | final double r = getNumberOfSuccesses(); |
| 273 | final double pInv = 1 - p; |
| 274 | return ( r * p ) / (pInv * pInv); |
| 275 | } |
| 276 | } |