| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math.distribution; |
| |
| import java.io.Serializable; |
| |
| import org.apache.commons.math.MathException; |
| import org.apache.commons.math.MathRuntimeException; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.random.RandomDataImpl; |
| import org.apache.commons.math.util.FastMath; |
| |
| |
| /** |
| * Base class for integer-valued discrete distributions. Default |
| * implementations are provided for some of the methods that do not vary |
| * from distribution to distribution. |
| * |
| * @version $Revision: 1067494 $ $Date: 2011-02-05 20:49:07 +0100 (sam. 05 févr. 2011) $ |
| */ |
| public abstract class AbstractIntegerDistribution extends AbstractDistribution |
| implements IntegerDistribution, Serializable { |
| |
| /** Serializable version identifier */ |
| private static final long serialVersionUID = -1146319659338487221L; |
| |
| /** |
| * RandomData instance used to generate samples from the distribution |
| * @since 2.2 |
| */ |
| protected final RandomDataImpl randomData = new RandomDataImpl(); |
| |
| /** |
| * Default constructor. |
| */ |
| protected AbstractIntegerDistribution() { |
| super(); |
| } |
| |
| /** |
| * For a random variable X whose values are distributed according |
| * to this distribution, this method returns P(X ≤ x). In other words, |
| * this method represents the (cumulative) distribution function, or |
| * CDF, for this distribution. |
| * <p> |
| * If <code>x</code> does not represent an integer value, the CDF is |
| * evaluated at the greatest integer less than x. |
| * |
| * @param x the value at which the distribution function is evaluated. |
| * @return cumulative probability that a random variable with this |
| * distribution takes a value less than or equal to <code>x</code> |
| * @throws MathException if the cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| */ |
| public double cumulativeProbability(double x) throws MathException { |
| return cumulativeProbability((int) FastMath.floor(x)); |
| } |
| |
| /** |
| * For a random variable X whose values are distributed according |
| * to this distribution, this method returns P(x0 ≤ X ≤ x1). |
| * |
| * @param x0 the (inclusive) lower bound |
| * @param x1 the (inclusive) upper bound |
| * @return the probability that a random variable with this distribution |
| * will take a value between <code>x0</code> and <code>x1</code>, |
| * including the endpoints. |
| * @throws MathException if the cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| * @throws IllegalArgumentException if <code>x0 > x1</code> |
| */ |
| @Override |
| public double cumulativeProbability(double x0, double x1) |
| throws MathException { |
| if (x0 > x1) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, x0, x1); |
| } |
| if (FastMath.floor(x0) < x0) { |
| return cumulativeProbability(((int) FastMath.floor(x0)) + 1, |
| (int) FastMath.floor(x1)); // don't want to count mass below x0 |
| } else { // x0 is mathematical integer, so use as is |
| return cumulativeProbability((int) FastMath.floor(x0), |
| (int) FastMath.floor(x1)); |
| } |
| } |
| |
| /** |
| * For a random variable X whose values are distributed according |
| * to this distribution, this method returns P(X ≤ x). In other words, |
| * this method represents the probability distribution function, or PDF, |
| * for this distribution. |
| * |
| * @param x the value at which the PDF is evaluated. |
| * @return PDF for this distribution. |
| * @throws MathException if the cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| */ |
| public abstract double cumulativeProbability(int x) throws MathException; |
| |
| /** |
| * For a random variable X whose values are distributed according |
| * to this distribution, this method returns P(X = x). In other words, this |
| * method represents the probability mass function, or PMF, for the distribution. |
| * <p> |
| * If <code>x</code> does not represent an integer value, 0 is returned. |
| * |
| * @param x the value at which the probability density function is evaluated |
| * @return the value of the probability density function at x |
| */ |
| public double probability(double x) { |
| double fl = FastMath.floor(x); |
| if (fl == x) { |
| return this.probability((int) x); |
| } else { |
| return 0; |
| } |
| } |
| |
| /** |
| * For a random variable X whose values are distributed according |
| * to this distribution, this method returns P(x0 ≤ X ≤ x1). |
| * |
| * @param x0 the inclusive, lower bound |
| * @param x1 the inclusive, upper bound |
| * @return the cumulative probability. |
| * @throws MathException if the cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| * @throws IllegalArgumentException if x0 > x1 |
| */ |
| public double cumulativeProbability(int x0, int x1) throws MathException { |
| if (x0 > x1) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, x0, x1); |
| } |
| return cumulativeProbability(x1) - cumulativeProbability(x0 - 1); |
| } |
| |
| /** |
| * For a random variable X whose values are distributed according |
| * to this distribution, this method returns the largest x, such |
| * that P(X ≤ x) ≤ <code>p</code>. |
| * |
| * @param p the desired probability |
| * @return the largest x such that P(X ≤ x) <= p |
| * @throws MathException if the inverse cumulative probability can not be |
| * computed due to convergence or other numerical errors. |
| * @throws IllegalArgumentException if p < 0 or p > 1 |
| */ |
| public int inverseCumulativeProbability(final double p) throws MathException{ |
| if (p < 0.0 || p > 1.0) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0); |
| } |
| |
| // by default, do simple bisection. |
| // subclasses can override if there is a better method. |
| int x0 = getDomainLowerBound(p); |
| int x1 = getDomainUpperBound(p); |
| double pm; |
| while (x0 < x1) { |
| int xm = x0 + (x1 - x0) / 2; |
| pm = checkedCumulativeProbability(xm); |
| if (pm > p) { |
| // update x1 |
| if (xm == x1) { |
| // this can happen with integer division |
| // simply decrement x1 |
| --x1; |
| } else { |
| // update x1 normally |
| x1 = xm; |
| } |
| } else { |
| // update x0 |
| if (xm == x0) { |
| // this can happen with integer division |
| // simply increment x0 |
| ++x0; |
| } else { |
| // update x0 normally |
| x0 = xm; |
| } |
| } |
| } |
| |
| // insure x0 is the correct critical point |
| pm = checkedCumulativeProbability(x0); |
| while (pm > p) { |
| --x0; |
| pm = checkedCumulativeProbability(x0); |
| } |
| |
| return x0; |
| } |
| |
| /** |
| * Reseeds the random generator used to generate samples. |
| * |
| * @param seed the new seed |
| * @since 2.2 |
| */ |
| public void reseedRandomGenerator(long seed) { |
| randomData.reSeed(seed); |
| } |
| |
| /** |
| * Generates a random value sampled from this distribution. The default |
| * implementation uses the |
| * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> inversion method.</a> |
| * |
| * @return random value |
| * @since 2.2 |
| * @throws MathException if an error occurs generating the random value |
| */ |
| public int sample() throws MathException { |
| return randomData.nextInversionDeviate(this); |
| } |
| |
| /** |
| * Generates a random sample from the distribution. The default implementation |
| * generates the sample by calling {@link #sample()} in a loop. |
| * |
| * @param sampleSize number of random values to generate |
| * @since 2.2 |
| * @return an array representing the random sample |
| * @throws MathException if an error occurs generating the sample |
| * @throws IllegalArgumentException if sampleSize is not positive |
| */ |
| public int[] sample(int sampleSize) throws MathException { |
| if (sampleSize <= 0) { |
| MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SAMPLE_SIZE, sampleSize); |
| } |
| int[] out = new int[sampleSize]; |
| for (int i = 0; i < sampleSize; i++) { |
| out[i] = sample(); |
| } |
| return out; |
| } |
| |
| /** |
| * Computes the cumulative probability function and checks for NaN values returned. |
| * Throws MathException if the value is NaN. Rethrows any MathException encountered |
| * evaluating the cumulative probability function. Throws |
| * MathException if the cumulative probability function returns NaN. |
| * |
| * @param argument input value |
| * @return cumulative probability |
| * @throws MathException if the cumulative probability is NaN |
| */ |
| private double checkedCumulativeProbability(int argument) throws MathException { |
| double result = Double.NaN; |
| result = cumulativeProbability(argument); |
| if (Double.isNaN(result)) { |
| throw new MathException(LocalizedFormats.DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument); |
| } |
| return result; |
| } |
| |
| /** |
| * Access the domain value lower bound, based on <code>p</code>, used to |
| * bracket a PDF root. This method is used by |
| * {@link #inverseCumulativeProbability(double)} to find critical values. |
| * |
| * @param p the desired probability for the critical value |
| * @return domain value lower bound, i.e. |
| * P(X < <i>lower bound</i>) < <code>p</code> |
| */ |
| protected abstract int getDomainLowerBound(double p); |
| |
| /** |
| * Access the domain value upper bound, based on <code>p</code>, used to |
| * bracket a PDF root. This method is used by |
| * {@link #inverseCumulativeProbability(double)} to find critical values. |
| * |
| * @param p the desired probability for the critical value |
| * @return domain value upper bound, i.e. |
| * P(X < <i>upper bound</i>) > <code>p</code> |
| */ |
| protected abstract int getDomainUpperBound(double p); |
| |
| /** |
| * Use this method to get information about whether the lower bound |
| * of the support is inclusive or not. For discrete support, |
| * only true here is meaningful. |
| * |
| * @return true (always but at Integer.MIN_VALUE because of the nature of discrete support) |
| * @since 2.2 |
| */ |
| public boolean isSupportLowerBoundInclusive() { |
| return true; |
| } |
| |
| /** |
| * Use this method to get information about whether the upper bound |
| * of the support is inclusive or not. For discrete support, |
| * only true here is meaningful. |
| * |
| * @return true (always but at Integer.MAX_VALUE because of the nature of discrete support) |
| * @since 2.2 |
| */ |
| public boolean isSupportUpperBoundInclusive() { |
| return true; |
| } |
| } |
