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 package org.apache.commons.math.distribution;
018
019 import java.io.Serializable;
020
021 import org.apache.commons.math.FunctionEvaluationException;
022 import org.apache.commons.math.MathException;
023 import org.apache.commons.math.MathRuntimeException;
024
025
026 /**
027 * Base class for integer-valued discrete distributions. Default
028 * implementations are provided for some of the methods that do not vary
029 * from distribution to distribution.
030 *
031 * @version $Revision: 920558 $ $Date: 2010-03-08 17:57:32 -0500 (Mon, 08 Mar 2010) $
032 */
033 public abstract class AbstractIntegerDistribution extends AbstractDistribution
034 implements IntegerDistribution, Serializable {
035
036 /** Message for endpoints in wrong order. */
037 private static final String WRONG_ORDER_ENDPOINTS_MESSAGE =
038 "lower endpoint ({0}) must be less than or equal to upper endpoint ({1})";
039
040 /** Message for out of range point. */
041 private static final String OUT_OF_RANGE_POINT =
042 "{0} out of [{1}, {2}] range";
043
044 /** Serializable version identifier */
045 private static final long serialVersionUID = -1146319659338487221L;
046
047 /**
048 * Default constructor.
049 */
050 protected AbstractIntegerDistribution() {
051 super();
052 }
053
054 /**
055 * For a random variable X whose values are distributed according
056 * to this distribution, this method returns P(X ≤ x). In other words,
057 * this method represents the (cumulative) distribution function, or
058 * CDF, for this distribution.
059 * <p>
060 * If <code>x</code> does not represent an integer value, the CDF is
061 * evaluated at the greatest integer less than x.
062 *
063 * @param x the value at which the distribution function is evaluated.
064 * @return cumulative probability that a random variable with this
065 * distribution takes a value less than or equal to <code>x</code>
066 * @throws MathException if the cumulative probability can not be
067 * computed due to convergence or other numerical errors.
068 */
069 public double cumulativeProbability(double x) throws MathException {
070 return cumulativeProbability((int) Math.floor(x));
071 }
072
073 /**
074 * For a random variable X whose values are distributed according
075 * to this distribution, this method returns P(x0 ≤ X ≤ x1).
076 *
077 * @param x0 the (inclusive) lower bound
078 * @param x1 the (inclusive) upper bound
079 * @return the probability that a random variable with this distribution
080 * will take a value between <code>x0</code> and <code>x1</code>,
081 * including the endpoints.
082 * @throws MathException if the cumulative probability can not be
083 * computed due to convergence or other numerical errors.
084 * @throws IllegalArgumentException if <code>x0 > x1</code>
085 */
086 @Override
087 public double cumulativeProbability(double x0, double x1)
088 throws MathException {
089 if (x0 > x1) {
090 throw MathRuntimeException.createIllegalArgumentException(
091 WRONG_ORDER_ENDPOINTS_MESSAGE, x0, x1);
092 }
093 if (Math.floor(x0) < x0) {
094 return cumulativeProbability(((int) Math.floor(x0)) + 1,
095 (int) Math.floor(x1)); // don't want to count mass below x0
096 } else { // x0 is mathematical integer, so use as is
097 return cumulativeProbability((int) Math.floor(x0),
098 (int) Math.floor(x1));
099 }
100 }
101
102 /**
103 * For a random variable X whose values are distributed according
104 * to this distribution, this method returns P(X ≤ x). In other words,
105 * this method represents the probability distribution function, or PDF,
106 * for this distribution.
107 *
108 * @param x the value at which the PDF is evaluated.
109 * @return PDF for this distribution.
110 * @throws MathException if the cumulative probability can not be
111 * computed due to convergence or other numerical errors.
112 */
113 public abstract double cumulativeProbability(int x) throws MathException;
114
115 /**
116 * For a random variable X whose values are distributed according
117 * to this distribution, this method returns P(X = x). In other words, this
118 * method represents the probability mass function, or PMF, for the distribution.
119 * <p>
120 * If <code>x</code> does not represent an integer value, 0 is returned.
121 *
122 * @param x the value at which the probability density function is evaluated
123 * @return the value of the probability density function at x
124 */
125 public double probability(double x) {
126 double fl = Math.floor(x);
127 if (fl == x) {
128 return this.probability((int) x);
129 } else {
130 return 0;
131 }
132 }
133
134 /**
135 * For a random variable X whose values are distributed according
136 * to this distribution, this method returns P(x0 ≤ X ≤ x1).
137 *
138 * @param x0 the inclusive, lower bound
139 * @param x1 the inclusive, upper bound
140 * @return the cumulative probability.
141 * @throws MathException if the cumulative probability can not be
142 * computed due to convergence or other numerical errors.
143 * @throws IllegalArgumentException if x0 > x1
144 */
145 public double cumulativeProbability(int x0, int x1) throws MathException {
146 if (x0 > x1) {
147 throw MathRuntimeException.createIllegalArgumentException(
148 WRONG_ORDER_ENDPOINTS_MESSAGE, x0, x1);
149 }
150 return cumulativeProbability(x1) - cumulativeProbability(x0 - 1);
151 }
152
153 /**
154 * For a random variable X whose values are distributed according
155 * to this distribution, this method returns the largest x, such
156 * that P(X ≤ x) ≤ <code>p</code>.
157 *
158 * @param p the desired probability
159 * @return the largest x such that P(X ≤ x) <= p
160 * @throws MathException if the inverse cumulative probability can not be
161 * computed due to convergence or other numerical errors.
162 * @throws IllegalArgumentException if p < 0 or p > 1
163 */
164 public int inverseCumulativeProbability(final double p) throws MathException{
165 if (p < 0.0 || p > 1.0) {
166 throw MathRuntimeException.createIllegalArgumentException(
167 OUT_OF_RANGE_POINT, p, 0.0, 1.0);
168 }
169
170 // by default, do simple bisection.
171 // subclasses can override if there is a better method.
172 int x0 = getDomainLowerBound(p);
173 int x1 = getDomainUpperBound(p);
174 double pm;
175 while (x0 < x1) {
176 int xm = x0 + (x1 - x0) / 2;
177 pm = checkedCumulativeProbability(xm);
178 if (pm > p) {
179 // update x1
180 if (xm == x1) {
181 // this can happen with integer division
182 // simply decrement x1
183 --x1;
184 } else {
185 // update x1 normally
186 x1 = xm;
187 }
188 } else {
189 // update x0
190 if (xm == x0) {
191 // this can happen with integer division
192 // simply increment x0
193 ++x0;
194 } else {
195 // update x0 normally
196 x0 = xm;
197 }
198 }
199 }
200
201 // insure x0 is the correct critical point
202 pm = checkedCumulativeProbability(x0);
203 while (pm > p) {
204 --x0;
205 pm = checkedCumulativeProbability(x0);
206 }
207
208 return x0;
209 }
210
211 /**
212 * Computes the cumulative probablity function and checks for NaN values returned.
213 * Throws MathException if the value is NaN. Wraps and rethrows any MathException encountered
214 * evaluating the cumulative probability function in a FunctionEvaluationException. Throws
215 * FunctionEvaluationException of the cumulative probability function returns NaN.
216 *
217 * @param argument input value
218 * @return cumulative probability
219 * @throws FunctionEvaluationException if a MathException occurs computing the cumulative probability
220 */
221 private double checkedCumulativeProbability(int argument) throws FunctionEvaluationException {
222 double result = Double.NaN;
223 try {
224 result = cumulativeProbability(argument);
225 } catch (MathException ex) {
226 throw new FunctionEvaluationException(ex, argument, ex.getPattern(), ex.getArguments());
227 }
228 if (Double.isNaN(result)) {
229 throw new FunctionEvaluationException(argument,
230 "Discrete cumulative probability function returned NaN for argument {0}", argument);
231 }
232 return result;
233 }
234
235 /**
236 * Access the domain value lower bound, based on <code>p</code>, used to
237 * bracket a PDF root. This method is used by
238 * {@link #inverseCumulativeProbability(double)} to find critical values.
239 *
240 * @param p the desired probability for the critical value
241 * @return domain value lower bound, i.e.
242 * P(X < <i>lower bound</i>) < <code>p</code>
243 */
244 protected abstract int getDomainLowerBound(double p);
245
246 /**
247 * Access the domain value upper bound, based on <code>p</code>, used to
248 * bracket a PDF root. This method is used by
249 * {@link #inverseCumulativeProbability(double)} to find critical values.
250 *
251 * @param p the desired probability for the critical value
252 * @return domain value upper bound, i.e.
253 * P(X < <i>upper bound</i>) > <code>p</code>
254 */
255 protected abstract int getDomainUpperBound(double p);
256 }