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
018package org.apache.commons.math3.random;
019
020import java.io.BufferedReader;
021import java.io.File;
022import java.io.FileInputStream;
023import java.io.IOException;
024import java.io.InputStream;
025import java.io.InputStreamReader;
026import java.net.URL;
027import java.nio.charset.Charset;
028import java.util.ArrayList;
029import java.util.List;
030
031import org.apache.commons.math3.distribution.AbstractRealDistribution;
032import org.apache.commons.math3.distribution.ConstantRealDistribution;
033import org.apache.commons.math3.distribution.NormalDistribution;
034import org.apache.commons.math3.distribution.RealDistribution;
035import org.apache.commons.math3.exception.MathIllegalStateException;
036import org.apache.commons.math3.exception.MathInternalError;
037import org.apache.commons.math3.exception.NullArgumentException;
038import org.apache.commons.math3.exception.OutOfRangeException;
039import org.apache.commons.math3.exception.ZeroException;
040import org.apache.commons.math3.exception.util.LocalizedFormats;
041import org.apache.commons.math3.stat.descriptive.StatisticalSummary;
042import org.apache.commons.math3.stat.descriptive.SummaryStatistics;
043import org.apache.commons.math3.util.FastMath;
044import org.apache.commons.math3.util.MathUtils;
045
046/**
047 * <p>Represents an <a href="http://http://en.wikipedia.org/wiki/Empirical_distribution_function">
048 * empirical probability distribution</a> -- a probability distribution derived
049 * from observed data without making any assumptions about the functional form
050 * of the population distribution that the data come from.</p>
051 *
052 * <p>An <code>EmpiricalDistribution</code> maintains data structures, called
053 * <i>distribution digests</i>, that describe empirical distributions and
054 * support the following operations: <ul>
055 * <li>loading the distribution from a file of observed data values</li>
056 * <li>dividing the input data into "bin ranges" and reporting bin frequency
057 *     counts (data for histogram)</li>
058 * <li>reporting univariate statistics describing the full set of data values
059 *     as well as the observations within each bin</li>
060 * <li>generating random values from the distribution</li>
061 * </ul>
062 * Applications can use <code>EmpiricalDistribution</code> to build grouped
063 * frequency histograms representing the input data or to generate random values
064 * "like" those in the input file -- i.e., the values generated will follow the
065 * distribution of the values in the file.</p>
066 *
067 * <p>The implementation uses what amounts to the
068 * <a href="http://nedwww.ipac.caltech.edu/level5/March02/Silverman/Silver2_6.html">
069 * Variable Kernel Method</a> with Gaussian smoothing:<p>
070 * <strong>Digesting the input file</strong>
071 * <ol><li>Pass the file once to compute min and max.</li>
072 * <li>Divide the range from min-max into <code>binCount</code> "bins."</li>
073 * <li>Pass the data file again, computing bin counts and univariate
074 *     statistics (mean, std dev.) for each of the bins </li>
075 * <li>Divide the interval (0,1) into subintervals associated with the bins,
076 *     with the length of a bin's subinterval proportional to its count.</li></ol>
077 * <strong>Generating random values from the distribution</strong><ol>
078 * <li>Generate a uniformly distributed value in (0,1) </li>
079 * <li>Select the subinterval to which the value belongs.
080 * <li>Generate a random Gaussian value with mean = mean of the associated
081 *     bin and std dev = std dev of associated bin.</li></ol></p>
082 *
083 * <p>EmpiricalDistribution implements the {@link RealDistribution} interface
084 * as follows.  Given x within the range of values in the dataset, let B
085 * be the bin containing x and let K be the within-bin kernel for B.  Let P(B-)
086 * be the sum of the probabilities of the bins below B and let K(B) be the
087 * mass of B under K (i.e., the integral of the kernel density over B).  Then
088 * set P(X < x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution
089 * evaluated at x. This results in a cdf that matches the grouped frequency
090 * distribution at the bin endpoints and interpolates within bins using
091 * within-bin kernels.</p>
092 *
093 *<strong>USAGE NOTES:</strong><ul>
094 *<li>The <code>binCount</code> is set by default to 1000.  A good rule of thumb
095 *    is to set the bin count to approximately the length of the input file divided
096 *    by 10. </li>
097 *<li>The input file <i>must</i> be a plain text file containing one valid numeric
098 *    entry per line.</li>
099 * </ul></p>
100 *
101 */
102public class EmpiricalDistribution extends AbstractRealDistribution {
103
104    /** Default bin count */
105    public static final int DEFAULT_BIN_COUNT = 1000;
106
107    /** Character set for file input */
108    private static final String FILE_CHARSET = "US-ASCII";
109
110    /** Serializable version identifier */
111    private static final long serialVersionUID = 5729073523949762654L;
112
113    /** RandomDataGenerator instance to use in repeated calls to getNext() */
114    protected final RandomDataGenerator randomData;
115
116    /** List of SummaryStatistics objects characterizing the bins */
117    private final List<SummaryStatistics> binStats;
118
119    /** Sample statistics */
120    private SummaryStatistics sampleStats = null;
121
122    /** Max loaded value */
123    private double max = Double.NEGATIVE_INFINITY;
124
125    /** Min loaded value */
126    private double min = Double.POSITIVE_INFINITY;
127
128    /** Grid size */
129    private double delta = 0d;
130
131    /** number of bins */
132    private final int binCount;
133
134    /** is the distribution loaded? */
135    private boolean loaded = false;
136
137    /** upper bounds of subintervals in (0,1) "belonging" to the bins */
138    private double[] upperBounds = null;
139
140    /**
141     * Creates a new EmpiricalDistribution with the default bin count.
142     */
143    public EmpiricalDistribution() {
144        this(DEFAULT_BIN_COUNT);
145    }
146
147    /**
148     * Creates a new EmpiricalDistribution with the specified bin count.
149     *
150     * @param binCount number of bins
151     */
152    public EmpiricalDistribution(int binCount) {
153        this(binCount, new RandomDataGenerator());
154    }
155
156    /**
157     * Creates a new EmpiricalDistribution with the specified bin count using the
158     * provided {@link RandomGenerator} as the source of random data.
159     *
160     * @param binCount number of bins
161     * @param generator random data generator (may be null, resulting in default JDK generator)
162     * @since 3.0
163     */
164    public EmpiricalDistribution(int binCount, RandomGenerator generator) {
165        this(binCount, new RandomDataGenerator(generator));
166    }
167
168    /**
169     * Creates a new EmpiricalDistribution with default bin count using the
170     * provided {@link RandomGenerator} as the source of random data.
171     *
172     * @param generator random data generator (may be null, resulting in default JDK generator)
173     * @since 3.0
174     */
175    public EmpiricalDistribution(RandomGenerator generator) {
176        this(DEFAULT_BIN_COUNT, generator);
177    }
178
179    /**
180     * Creates a new EmpiricalDistribution with the specified bin count using the
181     * provided {@link RandomDataImpl} instance as the source of random data.
182     *
183     * @param binCount number of bins
184     * @param randomData random data generator (may be null, resulting in default JDK generator)
185     * @since 3.0
186     * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(int,RandomGenerator)} instead.
187     */
188    @Deprecated
189    public EmpiricalDistribution(int binCount, RandomDataImpl randomData) {
190        this(binCount, randomData.getDelegate());
191    }
192
193    /**
194     * Creates a new EmpiricalDistribution with default bin count using the
195     * provided {@link RandomDataImpl} as the source of random data.
196     *
197     * @param randomData random data generator (may be null, resulting in default JDK generator)
198     * @since 3.0
199     * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(RandomGenerator)} instead.
200     */
201    @Deprecated
202    public EmpiricalDistribution(RandomDataImpl randomData) {
203        this(DEFAULT_BIN_COUNT, randomData);
204    }
205
206    /**
207     * Private constructor to allow lazy initialisation of the RNG contained
208     * in the {@link #randomData} instance variable.
209     *
210     * @param binCount number of bins
211     * @param randomData Random data generator.
212     */
213    private EmpiricalDistribution(int binCount,
214                                  RandomDataGenerator randomData) {
215        super(randomData.getRandomGenerator());
216        this.binCount = binCount;
217        this.randomData = randomData;
218        binStats = new ArrayList<SummaryStatistics>();
219    }
220
221    /**
222     * Computes the empirical distribution from the provided
223     * array of numbers.
224     *
225     * @param in the input data array
226     * @exception NullArgumentException if in is null
227     */
228    public void load(double[] in) throws NullArgumentException {
229        DataAdapter da = new ArrayDataAdapter(in);
230        try {
231            da.computeStats();
232            // new adapter for the second pass
233            fillBinStats(new ArrayDataAdapter(in));
234        } catch (IOException ex) {
235            // Can't happen
236            throw new MathInternalError();
237        }
238        loaded = true;
239
240    }
241
242    /**
243     * Computes the empirical distribution using data read from a URL.
244     *
245     * <p>The input file <i>must</i> be an ASCII text file containing one
246     * valid numeric entry per line.</p>
247     *
248     * @param url url of the input file
249     *
250     * @throws IOException if an IO error occurs
251     * @throws NullArgumentException if url is null
252     * @throws ZeroException if URL contains no data
253     */
254    public void load(URL url) throws IOException, NullArgumentException, ZeroException {
255        MathUtils.checkNotNull(url);
256        Charset charset = Charset.forName(FILE_CHARSET);
257        BufferedReader in =
258            new BufferedReader(new InputStreamReader(url.openStream(), charset));
259        try {
260            DataAdapter da = new StreamDataAdapter(in);
261            da.computeStats();
262            if (sampleStats.getN() == 0) {
263                throw new ZeroException(LocalizedFormats.URL_CONTAINS_NO_DATA, url);
264            }
265            // new adapter for the second pass
266            in = new BufferedReader(new InputStreamReader(url.openStream(), charset));
267            fillBinStats(new StreamDataAdapter(in));
268            loaded = true;
269        } finally {
270           try {
271               in.close();
272           } catch (IOException ex) { //NOPMD
273               // ignore
274           }
275        }
276    }
277
278    /**
279     * Computes the empirical distribution from the input file.
280     *
281     * <p>The input file <i>must</i> be an ASCII text file containing one
282     * valid numeric entry per line.</p>
283     *
284     * @param file the input file
285     * @throws IOException if an IO error occurs
286     * @throws NullArgumentException if file is null
287     */
288    public void load(File file) throws IOException, NullArgumentException {
289        MathUtils.checkNotNull(file);
290        Charset charset = Charset.forName(FILE_CHARSET);
291        InputStream is = new FileInputStream(file);
292        BufferedReader in = new BufferedReader(new InputStreamReader(is, charset));
293        try {
294            DataAdapter da = new StreamDataAdapter(in);
295            da.computeStats();
296            // new adapter for second pass
297            is = new FileInputStream(file);
298            in = new BufferedReader(new InputStreamReader(is, charset));
299            fillBinStats(new StreamDataAdapter(in));
300            loaded = true;
301        } finally {
302            try {
303                in.close();
304            } catch (IOException ex) { //NOPMD
305                // ignore
306            }
307        }
308    }
309
310    /**
311     * Provides methods for computing <code>sampleStats</code> and
312     * <code>beanStats</code> abstracting the source of data.
313     */
314    private abstract class DataAdapter{
315
316        /**
317         * Compute bin stats.
318         *
319         * @throws IOException  if an error occurs computing bin stats
320         */
321        public abstract void computeBinStats() throws IOException;
322
323        /**
324         * Compute sample statistics.
325         *
326         * @throws IOException if an error occurs computing sample stats
327         */
328        public abstract void computeStats() throws IOException;
329
330    }
331
332    /**
333     * <code>DataAdapter</code> for data provided through some input stream
334     */
335    private class StreamDataAdapter extends DataAdapter{
336
337        /** Input stream providing access to the data */
338        private BufferedReader inputStream;
339
340        /**
341         * Create a StreamDataAdapter from a BufferedReader
342         *
343         * @param in BufferedReader input stream
344         */
345        public StreamDataAdapter(BufferedReader in){
346            super();
347            inputStream = in;
348        }
349
350        /** {@inheritDoc} */
351        @Override
352        public void computeBinStats() throws IOException {
353            String str = null;
354            double val = 0.0d;
355            while ((str = inputStream.readLine()) != null) {
356                val = Double.parseDouble(str);
357                SummaryStatistics stats = binStats.get(findBin(val));
358                stats.addValue(val);
359            }
360
361            inputStream.close();
362            inputStream = null;
363        }
364
365        /** {@inheritDoc} */
366        @Override
367        public void computeStats() throws IOException {
368            String str = null;
369            double val = 0.0;
370            sampleStats = new SummaryStatistics();
371            while ((str = inputStream.readLine()) != null) {
372                val = Double.parseDouble(str);
373                sampleStats.addValue(val);
374            }
375            inputStream.close();
376            inputStream = null;
377        }
378    }
379
380    /**
381     * <code>DataAdapter</code> for data provided as array of doubles.
382     */
383    private class ArrayDataAdapter extends DataAdapter {
384
385        /** Array of input  data values */
386        private double[] inputArray;
387
388        /**
389         * Construct an ArrayDataAdapter from a double[] array
390         *
391         * @param in double[] array holding the data
392         * @throws NullArgumentException if in is null
393         */
394        public ArrayDataAdapter(double[] in) throws NullArgumentException {
395            super();
396            MathUtils.checkNotNull(in);
397            inputArray = in;
398        }
399
400        /** {@inheritDoc} */
401        @Override
402        public void computeStats() throws IOException {
403            sampleStats = new SummaryStatistics();
404            for (int i = 0; i < inputArray.length; i++) {
405                sampleStats.addValue(inputArray[i]);
406            }
407        }
408
409        /** {@inheritDoc} */
410        @Override
411        public void computeBinStats() throws IOException {
412            for (int i = 0; i < inputArray.length; i++) {
413                SummaryStatistics stats =
414                    binStats.get(findBin(inputArray[i]));
415                stats.addValue(inputArray[i]);
416            }
417        }
418    }
419
420    /**
421     * Fills binStats array (second pass through data file).
422     *
423     * @param da object providing access to the data
424     * @throws IOException  if an IO error occurs
425     */
426    private void fillBinStats(final DataAdapter da)
427        throws IOException {
428        // Set up grid
429        min = sampleStats.getMin();
430        max = sampleStats.getMax();
431        delta = (max - min)/((double) binCount);
432
433        // Initialize binStats ArrayList
434        if (!binStats.isEmpty()) {
435            binStats.clear();
436        }
437        for (int i = 0; i < binCount; i++) {
438            SummaryStatistics stats = new SummaryStatistics();
439            binStats.add(i,stats);
440        }
441
442        // Filling data in binStats Array
443        da.computeBinStats();
444
445        // Assign upperBounds based on bin counts
446        upperBounds = new double[binCount];
447        upperBounds[0] =
448        ((double) binStats.get(0).getN()) / (double) sampleStats.getN();
449        for (int i = 1; i < binCount-1; i++) {
450            upperBounds[i] = upperBounds[i-1] +
451            ((double) binStats.get(i).getN()) / (double) sampleStats.getN();
452        }
453        upperBounds[binCount-1] = 1.0d;
454    }
455
456    /**
457     * Returns the index of the bin to which the given value belongs
458     *
459     * @param value  the value whose bin we are trying to find
460     * @return the index of the bin containing the value
461     */
462    private int findBin(double value) {
463        return FastMath.min(
464                FastMath.max((int) FastMath.ceil((value - min) / delta) - 1, 0),
465                binCount - 1);
466    }
467
468    /**
469     * Generates a random value from this distribution.
470     * <strong>Preconditions:</strong><ul>
471     * <li>the distribution must be loaded before invoking this method</li></ul>
472     * @return the random value.
473     * @throws MathIllegalStateException if the distribution has not been loaded
474     */
475    public double getNextValue() throws MathIllegalStateException {
476
477        if (!loaded) {
478            throw new MathIllegalStateException(LocalizedFormats.DISTRIBUTION_NOT_LOADED);
479        }
480
481        return sample();
482    }
483
484    /**
485     * Returns a {@link StatisticalSummary} describing this distribution.
486     * <strong>Preconditions:</strong><ul>
487     * <li>the distribution must be loaded before invoking this method</li></ul>
488     *
489     * @return the sample statistics
490     * @throws IllegalStateException if the distribution has not been loaded
491     */
492    public StatisticalSummary getSampleStats() {
493        return sampleStats;
494    }
495
496    /**
497     * Returns the number of bins.
498     *
499     * @return the number of bins.
500     */
501    public int getBinCount() {
502        return binCount;
503    }
504
505    /**
506     * Returns a List of {@link SummaryStatistics} instances containing
507     * statistics describing the values in each of the bins.  The list is
508     * indexed on the bin number.
509     *
510     * @return List of bin statistics.
511     */
512    public List<SummaryStatistics> getBinStats() {
513        return binStats;
514    }
515
516    /**
517     * <p>Returns a fresh copy of the array of upper bounds for the bins.
518     * Bins are: <br/>
519     * [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],...,
520     *  (upperBounds[binCount-2], upperBounds[binCount-1] = max].</p>
521     *
522     * <p>Note: In versions 1.0-2.0 of commons-math, this method
523     * incorrectly returned the array of probability generator upper
524     * bounds now returned by {@link #getGeneratorUpperBounds()}.</p>
525     *
526     * @return array of bin upper bounds
527     * @since 2.1
528     */
529    public double[] getUpperBounds() {
530        double[] binUpperBounds = new double[binCount];
531        for (int i = 0; i < binCount - 1; i++) {
532            binUpperBounds[i] = min + delta * (i + 1);
533        }
534        binUpperBounds[binCount - 1] = max;
535        return binUpperBounds;
536    }
537
538    /**
539     * <p>Returns a fresh copy of the array of upper bounds of the subintervals
540     * of [0,1] used in generating data from the empirical distribution.
541     * Subintervals correspond to bins with lengths proportional to bin counts.</p>
542     *
543     * <strong>Preconditions:</strong><ul>
544     * <li>the distribution must be loaded before invoking this method</li></ul>
545     *
546     * <p>In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned
547     * by {@link #getUpperBounds()}.</p>
548     *
549     * @since 2.1
550     * @return array of upper bounds of subintervals used in data generation
551     * @throws NullPointerException unless a {@code load} method has been
552     * called beforehand.
553     */
554    public double[] getGeneratorUpperBounds() {
555        int len = upperBounds.length;
556        double[] out = new double[len];
557        System.arraycopy(upperBounds, 0, out, 0, len);
558        return out;
559    }
560
561    /**
562     * Property indicating whether or not the distribution has been loaded.
563     *
564     * @return true if the distribution has been loaded
565     */
566    public boolean isLoaded() {
567        return loaded;
568    }
569
570    /**
571     * Reseeds the random number generator used by {@link #getNextValue()}.
572     *
573     * @param seed random generator seed
574     * @since 3.0
575     */
576    public void reSeed(long seed) {
577        randomData.reSeed(seed);
578    }
579
580    // Distribution methods ---------------------------
581
582    /**
583     * {@inheritDoc}
584     * @since 3.1
585     */
586    @Override
587    public double probability(double x) {
588        return 0;
589    }
590
591    /**
592     * {@inheritDoc}
593     *
594     * <p>Returns the kernel density normalized so that its integral over each bin
595     * equals the bin mass.</p>
596     *
597     * <p>Algorithm description: <ol>
598     * <li>Find the bin B that x belongs to.</li>
599     * <li>Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the
600     * integral of the kernel density over B).</li>
601     * <li>Return k(x) * P(B) / K(B), where k is the within-bin kernel density
602     * and P(B) is the mass of B.</li></ol></p>
603     * @since 3.1
604     */
605    public double density(double x) {
606        if (x < min || x > max) {
607            return 0d;
608        }
609        final int binIndex = findBin(x);
610        final RealDistribution kernel = getKernel(binStats.get(binIndex));
611        return kernel.density(x) * pB(binIndex) / kB(binIndex);
612    }
613
614    /**
615     * {@inheritDoc}
616     *
617     * <p>Algorithm description:<ol>
618     * <li>Find the bin B that x belongs to.</li>
619     * <li>Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B.</li>
620     * <li>Compute K(B) = the probability mass of B with respect to the within-bin kernel
621     * and K(B-) = the kernel distribution evaluated at the lower endpoint of B</li>
622     * <li>Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where
623     * K(x) is the within-bin kernel distribution function evaluated at x.</li></ol></p>
624     *
625     * @since 3.1
626     */
627    public double cumulativeProbability(double x) {
628        if (x < min) {
629            return 0d;
630        } else if (x >= max) {
631            return 1d;
632        }
633        final int binIndex = findBin(x);
634        final double pBminus = pBminus(binIndex);
635        final double pB = pB(binIndex);
636        final double[] binBounds = getUpperBounds();
637        final double kB = kB(binIndex);
638        final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
639        final RealDistribution kernel = k(x);
640        final double withinBinCum =
641            (kernel.cumulativeProbability(x) -  kernel.cumulativeProbability(lower)) / kB;
642        return pBminus + pB * withinBinCum;
643    }
644
645    /**
646     * {@inheritDoc}
647     *
648     * <p>Algorithm description:<ol>
649     * <li>Find the smallest i such that the sum of the masses of the bins
650     *  through i is at least p.</li>
651     * <li>
652     *   Let K be the within-bin kernel distribution for bin i.</br>
653     *   Let K(B) be the mass of B under K. <br/>
654     *   Let K(B-) be K evaluated at the lower endpoint of B (the combined
655     *   mass of the bins below B under K).<br/>
656     *   Let P(B) be the probability of bin i.<br/>
657     *   Let P(B-) be the sum of the bin masses below bin i. <br/>
658     *   Let pCrit = p - P(B-)<br/>
659     * <li>Return the inverse of K evaluated at <br/>
660     *    K(B-) + pCrit * K(B) / P(B) </li>
661     *  </ol></p>
662     *
663     * @since 3.1
664     */
665    @Override
666    public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
667        if (p < 0.0 || p > 1.0) {
668            throw new OutOfRangeException(p, 0, 1);
669        }
670
671        if (p == 0.0) {
672            return getSupportLowerBound();
673        }
674
675        if (p == 1.0) {
676            return getSupportUpperBound();
677        }
678
679        int i = 0;
680        while (cumBinP(i) < p) {
681            i++;
682        }
683
684        final RealDistribution kernel = getKernel(binStats.get(i));
685        final double kB = kB(i);
686        final double[] binBounds = getUpperBounds();
687        final double lower = i == 0 ? min : binBounds[i - 1];
688        final double kBminus = kernel.cumulativeProbability(lower);
689        final double pB = pB(i);
690        final double pBminus = pBminus(i);
691        final double pCrit = p - pBminus;
692        if (pCrit <= 0) {
693            return lower;
694        }
695        return kernel.inverseCumulativeProbability(kBminus + pCrit * kB / pB);
696    }
697
698    /**
699     * {@inheritDoc}
700     * @since 3.1
701     */
702    public double getNumericalMean() {
703       return sampleStats.getMean();
704    }
705
706    /**
707     * {@inheritDoc}
708     * @since 3.1
709     */
710    public double getNumericalVariance() {
711        return sampleStats.getVariance();
712    }
713
714    /**
715     * {@inheritDoc}
716     * @since 3.1
717     */
718    public double getSupportLowerBound() {
719       return min;
720    }
721
722    /**
723     * {@inheritDoc}
724     * @since 3.1
725     */
726    public double getSupportUpperBound() {
727        return max;
728    }
729
730    /**
731     * {@inheritDoc}
732     * @since 3.1
733     */
734    public boolean isSupportLowerBoundInclusive() {
735        return true;
736    }
737
738    /**
739     * {@inheritDoc}
740     * @since 3.1
741     */
742    public boolean isSupportUpperBoundInclusive() {
743        return true;
744    }
745
746    /**
747     * {@inheritDoc}
748     * @since 3.1
749     */
750    public boolean isSupportConnected() {
751        return true;
752    }
753
754    /**
755     * {@inheritDoc}
756     * @since 3.1
757     */
758    @Override
759    public void reseedRandomGenerator(long seed) {
760        randomData.reSeed(seed);
761    }
762
763    /**
764     * The probability of bin i.
765     *
766     * @param i the index of the bin
767     * @return the probability that selection begins in bin i
768     */
769    private double pB(int i) {
770        return i == 0 ? upperBounds[0] :
771            upperBounds[i] - upperBounds[i - 1];
772    }
773
774    /**
775     * The combined probability of the bins up to but not including bin i.
776     *
777     * @param i the index of the bin
778     * @return the probability that selection begins in a bin below bin i.
779     */
780    private double pBminus(int i) {
781        return i == 0 ? 0 : upperBounds[i - 1];
782    }
783
784    /**
785     * Mass of bin i under the within-bin kernel of the bin.
786     *
787     * @param i index of the bin
788     * @return the difference in the within-bin kernel cdf between the
789     * upper and lower endpoints of bin i
790     */
791    @SuppressWarnings("deprecation")
792    private double kB(int i) {
793        final double[] binBounds = getUpperBounds();
794        final RealDistribution kernel = getKernel(binStats.get(i));
795        return i == 0 ? kernel.cumulativeProbability(min, binBounds[0]) :
796            kernel.cumulativeProbability(binBounds[i - 1], binBounds[i]);
797    }
798
799    /**
800     * The within-bin kernel of the bin that x belongs to.
801     *
802     * @param x the value to locate within a bin
803     * @return the within-bin kernel of the bin containing x
804     */
805    private RealDistribution k(double x) {
806        final int binIndex = findBin(x);
807        return getKernel(binStats.get(binIndex));
808    }
809
810    /**
811     * The combined probability of the bins up to and including binIndex.
812     *
813     * @param binIndex maximum bin index
814     * @return sum of the probabilities of bins through binIndex
815     */
816    private double cumBinP(int binIndex) {
817        return upperBounds[binIndex];
818    }
819
820    /**
821     * The within-bin smoothing kernel. Returns a Gaussian distribution
822     * parameterized by {@code bStats}, unless the bin contains only one
823     * observation, in which case a constant distribution is returned.
824     *
825     * @param bStats summary statistics for the bin
826     * @return within-bin kernel parameterized by bStats
827     */
828    protected RealDistribution getKernel(SummaryStatistics bStats) {
829        if (bStats.getN() == 1) {
830            return new ConstantRealDistribution(bStats.getMean());
831        } else {
832            return new NormalDistribution(randomData.getRandomGenerator(),
833                bStats.getMean(), bStats.getStandardDeviation(),
834                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
835        }
836    }
837}