diff options
Diffstat (limited to 'src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java | 866 |
1 files changed, 866 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java b/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java new file mode 100644 index 0000000..9ed3f4a --- /dev/null +++ b/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java @@ -0,0 +1,866 @@ +/* + * 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.math3.random; + +import org.apache.commons.math3.distribution.AbstractRealDistribution; +import org.apache.commons.math3.distribution.ConstantRealDistribution; +import org.apache.commons.math3.distribution.NormalDistribution; +import org.apache.commons.math3.distribution.RealDistribution; +import org.apache.commons.math3.exception.MathIllegalStateException; +import org.apache.commons.math3.exception.MathInternalError; +import org.apache.commons.math3.exception.NotStrictlyPositiveException; +import org.apache.commons.math3.exception.NullArgumentException; +import org.apache.commons.math3.exception.OutOfRangeException; +import org.apache.commons.math3.exception.ZeroException; +import org.apache.commons.math3.exception.util.LocalizedFormats; +import org.apache.commons.math3.stat.descriptive.StatisticalSummary; +import org.apache.commons.math3.stat.descriptive.SummaryStatistics; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.MathUtils; + +import java.io.BufferedReader; +import java.io.File; +import java.io.FileInputStream; +import java.io.IOException; +import java.io.InputStream; +import java.io.InputStreamReader; +import java.net.URL; +import java.nio.charset.Charset; +import java.util.ArrayList; +import java.util.List; + +/** + * Represents an <a href="http://http://en.wikipedia.org/wiki/Empirical_distribution_function"> + * empirical probability distribution</a> -- a probability distribution derived from observed data + * without making any assumptions about the functional form of the population distribution that the + * data come from. + * + * <p>An <code>EmpiricalDistribution</code> maintains data structures, called <i>distribution + * digests</i>, that describe empirical distributions and support the following operations: + * + * <ul> + * <li>loading the distribution from a file of observed data values + * <li>dividing the input data into "bin ranges" and reporting bin frequency counts (data for + * histogram) + * <li>reporting univariate statistics describing the full set of data values as well as the + * observations within each bin + * <li>generating random values from the distribution + * </ul> + * + * Applications can use <code>EmpiricalDistribution</code> to build grouped frequency histograms + * representing the input data or to generate random values "like" those in the input file -- i.e., + * the values generated will follow the distribution of the values in the file. + * + * <p>The implementation uses what amounts to the <a + * href="http://nedwww.ipac.caltech.edu/level5/March02/Silverman/Silver2_6.html">Variable Kernel + * Method</a> with Gaussian smoothing: + * + * <p><strong>Digesting the input file</strong> + * + * <ol> + * <li>Pass the file once to compute min and max. + * <li>Divide the range from min-max into <code>binCount</code> "bins." + * <li>Pass the data file again, computing bin counts and univariate statistics (mean, std dev.) + * for each of the bins + * <li>Divide the interval (0,1) into subintervals associated with the bins, with the length of a + * bin's subinterval proportional to its count. + * </ol> + * + * <strong>Generating random values from the distribution</strong> + * + * <ol> + * <li>Generate a uniformly distributed value in (0,1) + * <li>Select the subinterval to which the value belongs. + * <li>Generate a random Gaussian value with mean = mean of the associated bin and std dev = std + * dev of associated bin. + * </ol> + * + * <p>EmpiricalDistribution implements the {@link RealDistribution} interface as follows. Given x + * within the range of values in the dataset, let B be the bin containing x and let K be the + * within-bin kernel for B. Let P(B-) be the sum of the probabilities of the bins below B and let + * K(B) be the mass of B under K (i.e., the integral of the kernel density over B). Then set P(X < + * x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution evaluated at x. This + * results in a cdf that matches the grouped frequency distribution at the bin endpoints and + * interpolates within bins using within-bin kernels. <strong>USAGE NOTES:</strong> + * + * <ul> + * <li>The <code>binCount</code> is set by default to 1000. A good rule of thumb is to set the bin + * count to approximately the length of the input file divided by 10. + * <li>The input file <i>must</i> be a plain text file containing one valid numeric entry per + * line. + * </ul> + */ +public class EmpiricalDistribution extends AbstractRealDistribution { + + /** Default bin count */ + public static final int DEFAULT_BIN_COUNT = 1000; + + /** Character set for file input */ + private static final String FILE_CHARSET = "US-ASCII"; + + /** Serializable version identifier */ + private static final long serialVersionUID = 5729073523949762654L; + + /** RandomDataGenerator instance to use in repeated calls to getNext() */ + protected final RandomDataGenerator randomData; + + /** List of SummaryStatistics objects characterizing the bins */ + private final List<SummaryStatistics> binStats; + + /** Sample statistics */ + private SummaryStatistics sampleStats = null; + + /** Max loaded value */ + private double max = Double.NEGATIVE_INFINITY; + + /** Min loaded value */ + private double min = Double.POSITIVE_INFINITY; + + /** Grid size */ + private double delta = 0d; + + /** number of bins */ + private final int binCount; + + /** is the distribution loaded? */ + private boolean loaded = false; + + /** upper bounds of subintervals in (0,1) "belonging" to the bins */ + private double[] upperBounds = null; + + /** Creates a new EmpiricalDistribution with the default bin count. */ + public EmpiricalDistribution() { + this(DEFAULT_BIN_COUNT); + } + + /** + * Creates a new EmpiricalDistribution with the specified bin count. + * + * @param binCount number of bins. Must be strictly positive. + * @throws NotStrictlyPositiveException if {@code binCount <= 0}. + */ + public EmpiricalDistribution(int binCount) { + this(binCount, new RandomDataGenerator()); + } + + /** + * Creates a new EmpiricalDistribution with the specified bin count using the provided {@link + * RandomGenerator} as the source of random data. + * + * @param binCount number of bins. Must be strictly positive. + * @param generator random data generator (may be null, resulting in default JDK generator) + * @throws NotStrictlyPositiveException if {@code binCount <= 0}. + * @since 3.0 + */ + public EmpiricalDistribution(int binCount, RandomGenerator generator) { + this(binCount, new RandomDataGenerator(generator)); + } + + /** + * Creates a new EmpiricalDistribution with default bin count using the provided {@link + * RandomGenerator} as the source of random data. + * + * @param generator random data generator (may be null, resulting in default JDK generator) + * @since 3.0 + */ + public EmpiricalDistribution(RandomGenerator generator) { + this(DEFAULT_BIN_COUNT, generator); + } + + /** + * Creates a new EmpiricalDistribution with the specified bin count using the provided {@link + * RandomDataImpl} instance as the source of random data. + * + * @param binCount number of bins + * @param randomData random data generator (may be null, resulting in default JDK generator) + * @since 3.0 + * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(int,RandomGenerator)} + * instead. + */ + @Deprecated + public EmpiricalDistribution(int binCount, RandomDataImpl randomData) { + this(binCount, randomData.getDelegate()); + } + + /** + * Creates a new EmpiricalDistribution with default bin count using the provided {@link + * RandomDataImpl} as the source of random data. + * + * @param randomData random data generator (may be null, resulting in default JDK generator) + * @since 3.0 + * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(RandomGenerator)} instead. + */ + @Deprecated + public EmpiricalDistribution(RandomDataImpl randomData) { + this(DEFAULT_BIN_COUNT, randomData); + } + + /** + * Private constructor to allow lazy initialisation of the RNG contained in the {@link + * #randomData} instance variable. + * + * @param binCount number of bins. Must be strictly positive. + * @param randomData Random data generator. + * @throws NotStrictlyPositiveException if {@code binCount <= 0}. + */ + private EmpiricalDistribution(int binCount, RandomDataGenerator randomData) { + super(randomData.getRandomGenerator()); + if (binCount <= 0) { + throw new NotStrictlyPositiveException(binCount); + } + this.binCount = binCount; + this.randomData = randomData; + binStats = new ArrayList<SummaryStatistics>(); + } + + /** + * Computes the empirical distribution from the provided array of numbers. + * + * @param in the input data array + * @exception NullArgumentException if in is null + */ + public void load(double[] in) throws NullArgumentException { + DataAdapter da = new ArrayDataAdapter(in); + try { + da.computeStats(); + // new adapter for the second pass + fillBinStats(new ArrayDataAdapter(in)); + } catch (IOException ex) { + // Can't happen + throw new MathInternalError(); + } + loaded = true; + } + + /** + * Computes the empirical distribution using data read from a URL. + * + * <p>The input file <i>must</i> be an ASCII text file containing one valid numeric entry per + * line. + * + * @param url url of the input file + * @throws IOException if an IO error occurs + * @throws NullArgumentException if url is null + * @throws ZeroException if URL contains no data + */ + public void load(URL url) throws IOException, NullArgumentException, ZeroException { + MathUtils.checkNotNull(url); + Charset charset = Charset.forName(FILE_CHARSET); + BufferedReader in = new BufferedReader(new InputStreamReader(url.openStream(), charset)); + try { + DataAdapter da = new StreamDataAdapter(in); + da.computeStats(); + if (sampleStats.getN() == 0) { + throw new ZeroException(LocalizedFormats.URL_CONTAINS_NO_DATA, url); + } + // new adapter for the second pass + in = new BufferedReader(new InputStreamReader(url.openStream(), charset)); + fillBinStats(new StreamDataAdapter(in)); + loaded = true; + } finally { + try { + in.close(); + } catch (IOException ex) { // NOPMD + // ignore + } + } + } + + /** + * Computes the empirical distribution from the input file. + * + * <p>The input file <i>must</i> be an ASCII text file containing one valid numeric entry per + * line. + * + * @param file the input file + * @throws IOException if an IO error occurs + * @throws NullArgumentException if file is null + */ + public void load(File file) throws IOException, NullArgumentException { + MathUtils.checkNotNull(file); + Charset charset = Charset.forName(FILE_CHARSET); + InputStream is = new FileInputStream(file); + BufferedReader in = new BufferedReader(new InputStreamReader(is, charset)); + try { + DataAdapter da = new StreamDataAdapter(in); + da.computeStats(); + // new adapter for second pass + is = new FileInputStream(file); + in = new BufferedReader(new InputStreamReader(is, charset)); + fillBinStats(new StreamDataAdapter(in)); + loaded = true; + } finally { + try { + in.close(); + } catch (IOException ex) { // NOPMD + // ignore + } + } + } + + /** + * Provides methods for computing <code>sampleStats</code> and <code>beanStats</code> + * abstracting the source of data. + */ + private abstract class DataAdapter { + + /** + * Compute bin stats. + * + * @throws IOException if an error occurs computing bin stats + */ + public abstract void computeBinStats() throws IOException; + + /** + * Compute sample statistics. + * + * @throws IOException if an error occurs computing sample stats + */ + public abstract void computeStats() throws IOException; + } + + /** <code>DataAdapter</code> for data provided through some input stream */ + private class StreamDataAdapter extends DataAdapter { + + /** Input stream providing access to the data */ + private BufferedReader inputStream; + + /** + * Create a StreamDataAdapter from a BufferedReader + * + * @param in BufferedReader input stream + */ + StreamDataAdapter(BufferedReader in) { + super(); + inputStream = in; + } + + /** {@inheritDoc} */ + @Override + public void computeBinStats() throws IOException { + String str = null; + double val = 0.0d; + while ((str = inputStream.readLine()) != null) { + val = Double.parseDouble(str); + SummaryStatistics stats = binStats.get(findBin(val)); + stats.addValue(val); + } + + inputStream.close(); + inputStream = null; + } + + /** {@inheritDoc} */ + @Override + public void computeStats() throws IOException { + String str = null; + double val = 0.0; + sampleStats = new SummaryStatistics(); + while ((str = inputStream.readLine()) != null) { + val = Double.parseDouble(str); + sampleStats.addValue(val); + } + inputStream.close(); + inputStream = null; + } + } + + /** <code>DataAdapter</code> for data provided as array of doubles. */ + private class ArrayDataAdapter extends DataAdapter { + + /** Array of input data values */ + private double[] inputArray; + + /** + * Construct an ArrayDataAdapter from a double[] array + * + * @param in double[] array holding the data + * @throws NullArgumentException if in is null + */ + ArrayDataAdapter(double[] in) throws NullArgumentException { + super(); + MathUtils.checkNotNull(in); + inputArray = in; + } + + /** {@inheritDoc} */ + @Override + public void computeStats() throws IOException { + sampleStats = new SummaryStatistics(); + for (int i = 0; i < inputArray.length; i++) { + sampleStats.addValue(inputArray[i]); + } + } + + /** {@inheritDoc} */ + @Override + public void computeBinStats() throws IOException { + for (int i = 0; i < inputArray.length; i++) { + SummaryStatistics stats = binStats.get(findBin(inputArray[i])); + stats.addValue(inputArray[i]); + } + } + } + + /** + * Fills binStats array (second pass through data file). + * + * @param da object providing access to the data + * @throws IOException if an IO error occurs + */ + private void fillBinStats(final DataAdapter da) throws IOException { + // Set up grid + min = sampleStats.getMin(); + max = sampleStats.getMax(); + delta = (max - min) / ((double) binCount); + + // Initialize binStats ArrayList + if (!binStats.isEmpty()) { + binStats.clear(); + } + for (int i = 0; i < binCount; i++) { + SummaryStatistics stats = new SummaryStatistics(); + binStats.add(i, stats); + } + + // Filling data in binStats Array + da.computeBinStats(); + + // Assign upperBounds based on bin counts + upperBounds = new double[binCount]; + upperBounds[0] = ((double) binStats.get(0).getN()) / (double) sampleStats.getN(); + for (int i = 1; i < binCount - 1; i++) { + upperBounds[i] = + upperBounds[i - 1] + + ((double) binStats.get(i).getN()) / (double) sampleStats.getN(); + } + upperBounds[binCount - 1] = 1.0d; + } + + /** + * Returns the index of the bin to which the given value belongs + * + * @param value the value whose bin we are trying to find + * @return the index of the bin containing the value + */ + private int findBin(double value) { + return FastMath.min( + FastMath.max((int) FastMath.ceil((value - min) / delta) - 1, 0), binCount - 1); + } + + /** + * Generates a random value from this distribution. <strong>Preconditions:</strong> + * + * <ul> + * <li>the distribution must be loaded before invoking this method + * </ul> + * + * @return the random value. + * @throws MathIllegalStateException if the distribution has not been loaded + */ + public double getNextValue() throws MathIllegalStateException { + + if (!loaded) { + throw new MathIllegalStateException(LocalizedFormats.DISTRIBUTION_NOT_LOADED); + } + + return sample(); + } + + /** + * Returns a {@link StatisticalSummary} describing this distribution. + * <strong>Preconditions:</strong> + * + * <ul> + * <li>the distribution must be loaded before invoking this method + * </ul> + * + * @return the sample statistics + * @throws IllegalStateException if the distribution has not been loaded + */ + public StatisticalSummary getSampleStats() { + return sampleStats; + } + + /** + * Returns the number of bins. + * + * @return the number of bins. + */ + public int getBinCount() { + return binCount; + } + + /** + * Returns a List of {@link SummaryStatistics} instances containing statistics describing the + * values in each of the bins. The list is indexed on the bin number. + * + * @return List of bin statistics. + */ + public List<SummaryStatistics> getBinStats() { + return binStats; + } + + /** + * Returns a fresh copy of the array of upper bounds for the bins. Bins are: <br> + * [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],..., (upperBounds[binCount-2], + * upperBounds[binCount-1] = max]. + * + * <p>Note: In versions 1.0-2.0 of commons-math, this method incorrectly returned the array of + * probability generator upper bounds now returned by {@link #getGeneratorUpperBounds()}. + * + * @return array of bin upper bounds + * @since 2.1 + */ + public double[] getUpperBounds() { + double[] binUpperBounds = new double[binCount]; + for (int i = 0; i < binCount - 1; i++) { + binUpperBounds[i] = min + delta * (i + 1); + } + binUpperBounds[binCount - 1] = max; + return binUpperBounds; + } + + /** + * Returns a fresh copy of the array of upper bounds of the subintervals of [0,1] used in + * generating data from the empirical distribution. Subintervals correspond to bins with lengths + * proportional to bin counts. <strong>Preconditions:</strong> + * + * <ul> + * <li>the distribution must be loaded before invoking this method + * </ul> + * + * <p>In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned by {@link + * #getUpperBounds()}. + * + * @since 2.1 + * @return array of upper bounds of subintervals used in data generation + * @throws NullPointerException unless a {@code load} method has been called beforehand. + */ + public double[] getGeneratorUpperBounds() { + int len = upperBounds.length; + double[] out = new double[len]; + System.arraycopy(upperBounds, 0, out, 0, len); + return out; + } + + /** + * Property indicating whether or not the distribution has been loaded. + * + * @return true if the distribution has been loaded + */ + public boolean isLoaded() { + return loaded; + } + + /** + * Reseeds the random number generator used by {@link #getNextValue()}. + * + * @param seed random generator seed + * @since 3.0 + */ + public void reSeed(long seed) { + randomData.reSeed(seed); + } + + // Distribution methods --------------------------- + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + @Override + public double probability(double x) { + return 0; + } + + /** + * {@inheritDoc} + * + * <p>Returns the kernel density normalized so that its integral over each bin equals the bin + * mass. + * + * <p>Algorithm description: + * + * <ol> + * <li>Find the bin B that x belongs to. + * <li>Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the integral + * of the kernel density over B). + * <li>Return k(x) * P(B) / K(B), where k is the within-bin kernel density and P(B) is the + * mass of B. + * </ol> + * + * @since 3.1 + */ + public double density(double x) { + if (x < min || x > max) { + return 0d; + } + final int binIndex = findBin(x); + final RealDistribution kernel = getKernel(binStats.get(binIndex)); + return kernel.density(x) * pB(binIndex) / kB(binIndex); + } + + /** + * {@inheritDoc} + * + * <p>Algorithm description: + * + * <ol> + * <li>Find the bin B that x belongs to. + * <li>Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B. + * <li>Compute K(B) = the probability mass of B with respect to the within-bin kernel and + * K(B-) = the kernel distribution evaluated at the lower endpoint of B + * <li>Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where K(x) is the within-bin kernel + * distribution function evaluated at x. + * </ol> + * + * If K is a constant distribution, we return P(B-) + P(B) (counting the full mass of B). + * + * @since 3.1 + */ + public double cumulativeProbability(double x) { + if (x < min) { + return 0d; + } else if (x >= max) { + return 1d; + } + final int binIndex = findBin(x); + final double pBminus = pBminus(binIndex); + final double pB = pB(binIndex); + final RealDistribution kernel = k(x); + if (kernel instanceof ConstantRealDistribution) { + if (x < kernel.getNumericalMean()) { + return pBminus; + } else { + return pBminus + pB; + } + } + final double[] binBounds = getUpperBounds(); + final double kB = kB(binIndex); + final double lower = binIndex == 0 ? min : binBounds[binIndex - 1]; + final double withinBinCum = + (kernel.cumulativeProbability(x) - kernel.cumulativeProbability(lower)) / kB; + return pBminus + pB * withinBinCum; + } + + /** + * {@inheritDoc} + * + * <p>Algorithm description: + * + * <ol> + * <li>Find the smallest i such that the sum of the masses of the bins through i is at least + * p. + * <li>Let K be the within-bin kernel distribution for bin i.</br> Let K(B) be the mass of B + * under K. <br> + * Let K(B-) be K evaluated at the lower endpoint of B (the combined mass of the bins + * below B under K).<br> + * Let P(B) be the probability of bin i.<br> + * Let P(B-) be the sum of the bin masses below bin i. <br> + * Let pCrit = p - P(B-)<br> + * <li>Return the inverse of K evaluated at <br> + * K(B-) + pCrit * K(B) / P(B) + * </ol> + * + * @since 3.1 + */ + @Override + public double inverseCumulativeProbability(final double p) throws OutOfRangeException { + if (p < 0.0 || p > 1.0) { + throw new OutOfRangeException(p, 0, 1); + } + + if (p == 0.0) { + return getSupportLowerBound(); + } + + if (p == 1.0) { + return getSupportUpperBound(); + } + + int i = 0; + while (cumBinP(i) < p) { + i++; + } + + final RealDistribution kernel = getKernel(binStats.get(i)); + final double kB = kB(i); + final double[] binBounds = getUpperBounds(); + final double lower = i == 0 ? min : binBounds[i - 1]; + final double kBminus = kernel.cumulativeProbability(lower); + final double pB = pB(i); + final double pBminus = pBminus(i); + final double pCrit = p - pBminus; + if (pCrit <= 0) { + return lower; + } + return kernel.inverseCumulativeProbability(kBminus + pCrit * kB / pB); + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public double getNumericalMean() { + return sampleStats.getMean(); + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public double getNumericalVariance() { + return sampleStats.getVariance(); + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public double getSupportLowerBound() { + return min; + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public double getSupportUpperBound() { + return max; + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public boolean isSupportLowerBoundInclusive() { + return true; + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public boolean isSupportUpperBoundInclusive() { + return true; + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + public boolean isSupportConnected() { + return true; + } + + /** + * {@inheritDoc} + * + * @since 3.1 + */ + @Override + public void reseedRandomGenerator(long seed) { + randomData.reSeed(seed); + } + + /** + * The probability of bin i. + * + * @param i the index of the bin + * @return the probability that selection begins in bin i + */ + private double pB(int i) { + return i == 0 ? upperBounds[0] : upperBounds[i] - upperBounds[i - 1]; + } + + /** + * The combined probability of the bins up to but not including bin i. + * + * @param i the index of the bin + * @return the probability that selection begins in a bin below bin i. + */ + private double pBminus(int i) { + return i == 0 ? 0 : upperBounds[i - 1]; + } + + /** + * Mass of bin i under the within-bin kernel of the bin. + * + * @param i index of the bin + * @return the difference in the within-bin kernel cdf between the upper and lower endpoints of + * bin i + */ + @SuppressWarnings("deprecation") + private double kB(int i) { + final double[] binBounds = getUpperBounds(); + final RealDistribution kernel = getKernel(binStats.get(i)); + return i == 0 + ? kernel.cumulativeProbability(min, binBounds[0]) + : kernel.cumulativeProbability(binBounds[i - 1], binBounds[i]); + } + + /** + * The within-bin kernel of the bin that x belongs to. + * + * @param x the value to locate within a bin + * @return the within-bin kernel of the bin containing x + */ + private RealDistribution k(double x) { + final int binIndex = findBin(x); + return getKernel(binStats.get(binIndex)); + } + + /** + * The combined probability of the bins up to and including binIndex. + * + * @param binIndex maximum bin index + * @return sum of the probabilities of bins through binIndex + */ + private double cumBinP(int binIndex) { + return upperBounds[binIndex]; + } + + /** + * The within-bin smoothing kernel. Returns a Gaussian distribution parameterized by {@code + * bStats}, unless the bin contains only one observation, in which case a constant distribution + * is returned. + * + * @param bStats summary statistics for the bin + * @return within-bin kernel parameterized by bStats + */ + protected RealDistribution getKernel(SummaryStatistics bStats) { + if (bStats.getN() == 1 || bStats.getVariance() == 0) { + return new ConstantRealDistribution(bStats.getMean()); + } else { + return new NormalDistribution( + randomData.getRandomGenerator(), + bStats.getMean(), + bStats.getStandardDeviation(), + NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY); + } + } +} |