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Diffstat (limited to 'src/main/java/org/apache/commons/math/distribution/AbstractIntegerDistribution.java')
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diff --git a/src/main/java/org/apache/commons/math/distribution/AbstractIntegerDistribution.java b/src/main/java/org/apache/commons/math/distribution/AbstractIntegerDistribution.java new file mode 100644 index 0000000..96cfe5d --- /dev/null +++ b/src/main/java/org/apache/commons/math/distribution/AbstractIntegerDistribution.java @@ -0,0 +1,319 @@ +/* + * 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; + } +} |