source: src/main/java/agents/anac/y2019/harddealer/math3/random/EmpiricalDistribution.java

Last change on this file was 204, checked in by Katsuhide Fujita, 5 years ago

Fixed errors of ANAC2019 agents
  • Property svn:executable set to *
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1/*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17
18package agents.anac.y2019.harddealer.math3.random;
19
20import java.io.BufferedReader;
21import java.io.File;
22import java.io.FileInputStream;
23import java.io.IOException;
24import java.io.InputStream;
25import java.io.InputStreamReader;
26import java.net.URL;
27import java.nio.charset.Charset;
28import java.util.ArrayList;
29import java.util.List;
30
31import agents.anac.y2019.harddealer.math3.distribution.AbstractRealDistribution;
32import agents.anac.y2019.harddealer.math3.distribution.ConstantRealDistribution;
33import agents.anac.y2019.harddealer.math3.distribution.NormalDistribution;
34import agents.anac.y2019.harddealer.math3.distribution.RealDistribution;
35import agents.anac.y2019.harddealer.math3.exception.MathIllegalStateException;
36import agents.anac.y2019.harddealer.math3.exception.MathInternalError;
37import agents.anac.y2019.harddealer.math3.exception.NullArgumentException;
38import agents.anac.y2019.harddealer.math3.exception.OutOfRangeException;
39import agents.anac.y2019.harddealer.math3.exception.ZeroException;
40import agents.anac.y2019.harddealer.math3.exception.NotStrictlyPositiveException;
41import agents.anac.y2019.harddealer.math3.exception.util.LocalizedFormats;
42import agents.anac.y2019.harddealer.math3.stat.descriptive.StatisticalSummary;
43import agents.anac.y2019.harddealer.math3.stat.descriptive.SummaryStatistics;
44import agents.anac.y2019.harddealer.math3.util.FastMath;
45import agents.anac.y2019.harddealer.math3.util.MathUtils;
46
47/**
48 * <p>Represents an <a href="http://http://en.wikipedia.org/wiki/Empirical_distribution_function">
49 * empirical probability distribution</a> -- a probability distribution derived
50 * from observed data without making any assumptions about the functional form
51 * of the population distribution that the data come from.</p>
52 *
53 * <p>An <code>EmpiricalDistribution</code> maintains data structures, called
54 * <i>distribution digests</i>, that describe empirical distributions and
55 * support the following operations: <ul>
56 * <li>loading the distribution from a file of observed data values</li>
57 * <li>dividing the input data into "bin ranges" and reporting bin frequency
58 * counts (data for histogram)</li>
59 * <li>reporting univariate statistics describing the full set of data values
60 * as well as the observations within each bin</li>
61 * <li>generating random values from the distribution</li>
62 * </ul>
63 * Applications can use <code>EmpiricalDistribution</code> to build grouped
64 * frequency histograms representing the input data or to generate random values
65 * "like" those in the input file -- i.e., the values generated will follow the
66 * distribution of the values in the file.</p>
67 *
68 * <p>The implementation uses what amounts to the
69 * <a href="http://nedwww.ipac.caltech.edu/level5/March02/Silverman/Silver2_6.html">
70 * Variable Kernel Method</a> with Gaussian smoothing:<p>
71 * <strong>Digesting the input file</strong>
72 * <ol><li>Pass the file once to compute min and max.</li>
73 * <li>Divide the range from min-max into <code>binCount</code> "bins."</li>
74 * <li>Pass the data file again, computing bin counts and univariate
75 * statistics (mean, std dev.) for each of the bins </li>
76 * <li>Divide the interval (0,1) into subintervals associated with the bins,
77 * with the length of a bin's subinterval proportional to its count.</li></ol>
78 * <strong>Generating random values from the distribution</strong><ol>
79 * <li>Generate a uniformly distributed value in (0,1) </li>
80 * <li>Select the subinterval to which the value belongs.
81 * <li>Generate a random Gaussian value with mean = mean of the associated
82 * bin and std dev = std dev of associated bin.</li></ol></p>
83 *
84 * <p>EmpiricalDistribution implements the {@link RealDistribution} interface
85 * as follows. Given x within the range of values in the dataset, let B
86 * be the bin containing x and let K be the within-bin kernel for B. Let P(B-)
87 * be the sum of the probabilities of the bins below B and let K(B) be the
88 * mass of B under K (i.e., the integral of the kernel density over B). Then
89 * set P(X < x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution
90 * evaluated at x. This results in a cdf that matches the grouped frequency
91 * distribution at the bin endpoints and interpolates within bins using
92 * within-bin kernels.</p>
93 *
94 *<strong>USAGE NOTES:</strong><ul>
95 *<li>The <code>binCount</code> is set by default to 1000. A good rule of thumb
96 * is to set the bin count to approximately the length of the input file divided
97 * by 10. </li>
98 *<li>The input file <i>must</i> be a plain text file containing one valid numeric
99 * entry per line.</li>
100 * </ul></p>
101 *
102 */
103public class EmpiricalDistribution extends AbstractRealDistribution {
104
105 /** Default bin count */
106 public static final int DEFAULT_BIN_COUNT = 1000;
107
108 /** Character set for file input */
109 private static final String FILE_CHARSET = "US-ASCII";
110
111 /** Serializable version identifier */
112 private static final long serialVersionUID = 5729073523949762654L;
113
114 /** RandomDataGenerator instance to use in repeated calls to getNext() */
115 protected final RandomDataGenerator randomData;
116
117 /** List of SummaryStatistics objects characterizing the bins */
118 private final List<SummaryStatistics> binStats;
119
120 /** Sample statistics */
121 private SummaryStatistics sampleStats = null;
122
123 /** Max loaded value */
124 private double max = Double.NEGATIVE_INFINITY;
125
126 /** Min loaded value */
127 private double min = Double.POSITIVE_INFINITY;
128
129 /** Grid size */
130 private double delta = 0d;
131
132 /** number of bins */
133 private final int binCount;
134
135 /** is the distribution loaded? */
136 private boolean loaded = false;
137
138 /** upper bounds of subintervals in (0,1) "belonging" to the bins */
139 private double[] upperBounds = null;
140
141 /**
142 * Creates a new EmpiricalDistribution with the default bin count.
143 */
144 public EmpiricalDistribution() {
145 this(DEFAULT_BIN_COUNT);
146 }
147
148 /**
149 * Creates a new EmpiricalDistribution with the specified bin count.
150 *
151 * @param binCount number of bins. Must be strictly positive.
152 * @throws NotStrictlyPositiveException if {@code binCount <= 0}.
153 */
154 public EmpiricalDistribution(int binCount) {
155 this(binCount, new RandomDataGenerator());
156 }
157
158 /**
159 * Creates a new EmpiricalDistribution with the specified bin count using the
160 * provided {@link RandomGenerator} as the source of random data.
161 *
162 * @param binCount number of bins. Must be strictly positive.
163 * @param generator random data generator (may be null, resulting in default JDK generator)
164 * @throws NotStrictlyPositiveException if {@code binCount <= 0}.
165 * @since 3.0
166 */
167 public EmpiricalDistribution(int binCount, RandomGenerator generator) {
168 this(binCount, new RandomDataGenerator(generator));
169 }
170
171 /**
172 * Creates a new EmpiricalDistribution with default bin count using the
173 * provided {@link RandomGenerator} as the source of random data.
174 *
175 * @param generator random data generator (may be null, resulting in default JDK generator)
176 * @since 3.0
177 */
178 public EmpiricalDistribution(RandomGenerator generator) {
179 this(DEFAULT_BIN_COUNT, generator);
180 }
181
182 /**
183 * Creates a new EmpiricalDistribution with the specified bin count using the
184 * provided {@link RandomDataImpl} instance as the source of random data.
185 *
186 * @param binCount number of bins
187 * @param randomData random data generator (may be null, resulting in default JDK generator)
188 * @since 3.0
189 * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(int,RandomGenerator)} instead.
190 */
191 @Deprecated
192 public EmpiricalDistribution(int binCount, RandomDataImpl randomData) {
193 this(binCount, randomData.getDelegate());
194 }
195
196 /**
197 * Creates a new EmpiricalDistribution with default bin count using the
198 * provided {@link RandomDataImpl} as the source of random data.
199 *
200 * @param randomData random data generator (may be null, resulting in default JDK generator)
201 * @since 3.0
202 * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(RandomGenerator)} instead.
203 */
204 @Deprecated
205 public EmpiricalDistribution(RandomDataImpl randomData) {
206 this(DEFAULT_BIN_COUNT, randomData);
207 }
208
209 /**
210 * Private constructor to allow lazy initialisation of the RNG contained
211 * in the {@link #randomData} instance variable.
212 *
213 * @param binCount number of bins. Must be strictly positive.
214 * @param randomData Random data generator.
215 * @throws NotStrictlyPositiveException if {@code binCount <= 0}.
216 */
217 private EmpiricalDistribution(int binCount,
218 RandomDataGenerator randomData) {
219 super(randomData.getRandomGenerator());
220 if (binCount <= 0) {
221 throw new NotStrictlyPositiveException(binCount);
222 }
223 this.binCount = binCount;
224 this.randomData = randomData;
225 binStats = new ArrayList<SummaryStatistics>();
226 }
227
228 /**
229 * Computes the empirical distribution from the provided
230 * array of numbers.
231 *
232 * @param in the input data array
233 * @exception NullArgumentException if in is null
234 */
235 public void load(double[] in) throws NullArgumentException {
236 DataAdapter da = new ArrayDataAdapter(in);
237 try {
238 da.computeStats();
239 // new adapter for the second pass
240 fillBinStats(new ArrayDataAdapter(in));
241 } catch (IOException ex) {
242 // Can't happen
243 throw new MathInternalError();
244 }
245 loaded = true;
246
247 }
248
249 /**
250 * Computes the empirical distribution using data read from a URL.
251 *
252 * <p>The input file <i>must</i> be an ASCII text file containing one
253 * valid numeric entry per line.</p>
254 *
255 * @param url url of the input file
256 *
257 * @throws IOException if an IO error occurs
258 * @throws NullArgumentException if url is null
259 * @throws ZeroException if URL contains no data
260 */
261 public void load(URL url) throws IOException, NullArgumentException, ZeroException {
262 MathUtils.checkNotNull(url);
263 Charset charset = Charset.forName(FILE_CHARSET);
264 BufferedReader in =
265 new BufferedReader(new InputStreamReader(url.openStream(), charset));
266 try {
267 DataAdapter da = new StreamDataAdapter(in);
268 da.computeStats();
269 if (sampleStats.getN() == 0) {
270 throw new ZeroException(LocalizedFormats.URL_CONTAINS_NO_DATA, url);
271 }
272 // new adapter for the second pass
273 in = new BufferedReader(new InputStreamReader(url.openStream(), charset));
274 fillBinStats(new StreamDataAdapter(in));
275 loaded = true;
276 } finally {
277 try {
278 in.close();
279 } catch (IOException ex) { //NOPMD
280 // ignore
281 }
282 }
283 }
284
285 /**
286 * Computes the empirical distribution from the input file.
287 *
288 * <p>The input file <i>must</i> be an ASCII text file containing one
289 * valid numeric entry per line.</p>
290 *
291 * @param file the input file
292 * @throws IOException if an IO error occurs
293 * @throws NullArgumentException if file is null
294 */
295 public void load(File file) throws IOException, NullArgumentException {
296 MathUtils.checkNotNull(file);
297 Charset charset = Charset.forName(FILE_CHARSET);
298 InputStream is = new FileInputStream(file);
299 BufferedReader in = new BufferedReader(new InputStreamReader(is, charset));
300 try {
301 DataAdapter da = new StreamDataAdapter(in);
302 da.computeStats();
303 // new adapter for second pass
304 is = new FileInputStream(file);
305 in = new BufferedReader(new InputStreamReader(is, charset));
306 fillBinStats(new StreamDataAdapter(in));
307 loaded = true;
308 } finally {
309 try {
310 in.close();
311 } catch (IOException ex) { //NOPMD
312 // ignore
313 }
314 }
315 }
316
317 /**
318 * Provides methods for computing <code>sampleStats</code> and
319 * <code>beanStats</code> abstracting the source of data.
320 */
321 private abstract class DataAdapter{
322
323 /**
324 * Compute bin stats.
325 *
326 * @throws IOException if an error occurs computing bin stats
327 */
328 public abstract void computeBinStats() throws IOException;
329
330 /**
331 * Compute sample statistics.
332 *
333 * @throws IOException if an error occurs computing sample stats
334 */
335 public abstract void computeStats() throws IOException;
336
337 }
338
339 /**
340 * <code>DataAdapter</code> for data provided through some input stream
341 */
342 private class StreamDataAdapter extends DataAdapter{
343
344 /** Input stream providing access to the data */
345 private BufferedReader inputStream;
346
347 /**
348 * Create a StreamDataAdapter from a BufferedReader
349 *
350 * @param in BufferedReader input stream
351 */
352 StreamDataAdapter(BufferedReader in){
353 super();
354 inputStream = in;
355 }
356
357 /** {@inheritDoc} */
358 @Override
359 public void computeBinStats() throws IOException {
360 String str = null;
361 double val = 0.0d;
362 while ((str = inputStream.readLine()) != null) {
363 val = Double.parseDouble(str);
364 SummaryStatistics stats = binStats.get(findBin(val));
365 stats.addValue(val);
366 }
367
368 inputStream.close();
369 inputStream = null;
370 }
371
372 /** {@inheritDoc} */
373 @Override
374 public void computeStats() throws IOException {
375 String str = null;
376 double val = 0.0;
377 sampleStats = new SummaryStatistics();
378 while ((str = inputStream.readLine()) != null) {
379 val = Double.parseDouble(str);
380 sampleStats.addValue(val);
381 }
382 inputStream.close();
383 inputStream = null;
384 }
385 }
386
387 /**
388 * <code>DataAdapter</code> for data provided as array of doubles.
389 */
390 private class ArrayDataAdapter extends DataAdapter {
391
392 /** Array of input data values */
393 private double[] inputArray;
394
395 /**
396 * Construct an ArrayDataAdapter from a double[] array
397 *
398 * @param in double[] array holding the data
399 * @throws NullArgumentException if in is null
400 */
401 ArrayDataAdapter(double[] in) throws NullArgumentException {
402 super();
403 MathUtils.checkNotNull(in);
404 inputArray = in;
405 }
406
407 /** {@inheritDoc} */
408 @Override
409 public void computeStats() throws IOException {
410 sampleStats = new SummaryStatistics();
411 for (int i = 0; i < inputArray.length; i++) {
412 sampleStats.addValue(inputArray[i]);
413 }
414 }
415
416 /** {@inheritDoc} */
417 @Override
418 public void computeBinStats() throws IOException {
419 for (int i = 0; i < inputArray.length; i++) {
420 SummaryStatistics stats =
421 binStats.get(findBin(inputArray[i]));
422 stats.addValue(inputArray[i]);
423 }
424 }
425 }
426
427 /**
428 * Fills binStats array (second pass through data file).
429 *
430 * @param da object providing access to the data
431 * @throws IOException if an IO error occurs
432 */
433 private void fillBinStats(final DataAdapter da)
434 throws IOException {
435 // Set up grid
436 min = sampleStats.getMin();
437 max = sampleStats.getMax();
438 delta = (max - min)/((double) binCount);
439
440 // Initialize binStats ArrayList
441 if (!binStats.isEmpty()) {
442 binStats.clear();
443 }
444 for (int i = 0; i < binCount; i++) {
445 SummaryStatistics stats = new SummaryStatistics();
446 binStats.add(i,stats);
447 }
448
449 // Filling data in binStats Array
450 da.computeBinStats();
451
452 // Assign upperBounds based on bin counts
453 upperBounds = new double[binCount];
454 upperBounds[0] =
455 ((double) binStats.get(0).getN()) / (double) sampleStats.getN();
456 for (int i = 1; i < binCount-1; i++) {
457 upperBounds[i] = upperBounds[i-1] +
458 ((double) binStats.get(i).getN()) / (double) sampleStats.getN();
459 }
460 upperBounds[binCount-1] = 1.0d;
461 }
462
463 /**
464 * Returns the index of the bin to which the given value belongs
465 *
466 * @param value the value whose bin we are trying to find
467 * @return the index of the bin containing the value
468 */
469 private int findBin(double value) {
470 return FastMath.min(
471 FastMath.max((int) FastMath.ceil((value - min) / delta) - 1, 0),
472 binCount - 1);
473 }
474
475 /**
476 * Generates a random value from this distribution.
477 * <strong>Preconditions:</strong><ul>
478 * <li>the distribution must be loaded before invoking this method</li></ul>
479 * @return the random value.
480 * @throws MathIllegalStateException if the distribution has not been loaded
481 */
482 public double getNextValue() throws MathIllegalStateException {
483
484 if (!loaded) {
485 throw new MathIllegalStateException(LocalizedFormats.DISTRIBUTION_NOT_LOADED);
486 }
487
488 return sample();
489 }
490
491 /**
492 * Returns a {@link StatisticalSummary} describing this distribution.
493 * <strong>Preconditions:</strong><ul>
494 * <li>the distribution must be loaded before invoking this method</li></ul>
495 *
496 * @return the sample statistics
497 * @throws IllegalStateException if the distribution has not been loaded
498 */
499 public StatisticalSummary getSampleStats() {
500 return sampleStats;
501 }
502
503 /**
504 * Returns the number of bins.
505 *
506 * @return the number of bins.
507 */
508 public int getBinCount() {
509 return binCount;
510 }
511
512 /**
513 * Returns a List of {@link SummaryStatistics} instances containing
514 * statistics describing the values in each of the bins. The list is
515 * indexed on the bin number.
516 *
517 * @return List of bin statistics.
518 */
519 public List<SummaryStatistics> getBinStats() {
520 return binStats;
521 }
522
523 /**
524 * <p>Returns a fresh copy of the array of upper bounds for the bins.
525 * Bins are: <br/>
526 * [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],...,
527 * (upperBounds[binCount-2], upperBounds[binCount-1] = max].</p>
528 *
529 * <p>Note: In versions 1.0-2.0 of commons-math, this method
530 * incorrectly returned the array of probability generator upper
531 * bounds now returned by {@link #getGeneratorUpperBounds()}.</p>
532 *
533 * @return array of bin upper bounds
534 * @since 2.1
535 */
536 public double[] getUpperBounds() {
537 double[] binUpperBounds = new double[binCount];
538 for (int i = 0; i < binCount - 1; i++) {
539 binUpperBounds[i] = min + delta * (i + 1);
540 }
541 binUpperBounds[binCount - 1] = max;
542 return binUpperBounds;
543 }
544
545 /**
546 * <p>Returns a fresh copy of the array of upper bounds of the subintervals
547 * of [0,1] used in generating data from the empirical distribution.
548 * Subintervals correspond to bins with lengths proportional to bin counts.</p>
549 *
550 * <strong>Preconditions:</strong><ul>
551 * <li>the distribution must be loaded before invoking this method</li></ul>
552 *
553 * <p>In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned
554 * by {@link #getUpperBounds()}.</p>
555 *
556 * @since 2.1
557 * @return array of upper bounds of subintervals used in data generation
558 * @throws NullPointerException unless a {@code load} method has been
559 * called beforehand.
560 */
561 public double[] getGeneratorUpperBounds() {
562 int len = upperBounds.length;
563 double[] out = new double[len];
564 System.arraycopy(upperBounds, 0, out, 0, len);
565 return out;
566 }
567
568 /**
569 * Property indicating whether or not the distribution has been loaded.
570 *
571 * @return true if the distribution has been loaded
572 */
573 public boolean isLoaded() {
574 return loaded;
575 }
576
577 /**
578 * Reseeds the random number generator used by {@link #getNextValue()}.
579 *
580 * @param seed random generator seed
581 * @since 3.0
582 */
583 public void reSeed(long seed) {
584 randomData.reSeed(seed);
585 }
586
587 // Distribution methods ---------------------------
588
589 /**
590 * {@inheritDoc}
591 * @since 3.1
592 */
593 @Override
594 public double probability(double x) {
595 return 0;
596 }
597
598 /**
599 * {@inheritDoc}
600 *
601 * <p>Returns the kernel density normalized so that its integral over each bin
602 * equals the bin mass.</p>
603 *
604 * <p>Algorithm description: <ol>
605 * <li>Find the bin B that x belongs to.</li>
606 * <li>Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the
607 * integral of the kernel density over B).</li>
608 * <li>Return k(x) * P(B) / K(B), where k is the within-bin kernel density
609 * and P(B) is the mass of B.</li></ol></p>
610 * @since 3.1
611 */
612 public double density(double x) {
613 if (x < min || x > max) {
614 return 0d;
615 }
616 final int binIndex = findBin(x);
617 final RealDistribution kernel = getKernel(binStats.get(binIndex));
618 return kernel.density(x) * pB(binIndex) / kB(binIndex);
619 }
620
621 /**
622 * {@inheritDoc}
623 *
624 * <p>Algorithm description:<ol>
625 * <li>Find the bin B that x belongs to.</li>
626 * <li>Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B.</li>
627 * <li>Compute K(B) = the probability mass of B with respect to the within-bin kernel
628 * and K(B-) = the kernel distribution evaluated at the lower endpoint of B</li>
629 * <li>Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where
630 * K(x) is the within-bin kernel distribution function evaluated at x.</li></ol>
631 * If K is a constant distribution, we return P(B-) + P(B) (counting the full
632 * mass of B).</p>
633 *
634 * @since 3.1
635 */
636 public double cumulativeProbability(double x) {
637 if (x < min) {
638 return 0d;
639 } else if (x >= max) {
640 return 1d;
641 }
642 final int binIndex = findBin(x);
643 final double pBminus = pBminus(binIndex);
644 final double pB = pB(binIndex);
645 final RealDistribution kernel = k(x);
646 if (kernel instanceof ConstantRealDistribution) {
647 if (x < kernel.getNumericalMean()) {
648 return pBminus;
649 } else {
650 return pBminus + pB;
651 }
652 }
653 final double[] binBounds = getUpperBounds();
654 final double kB = kB(binIndex);
655 final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
656 final double withinBinCum =
657 (kernel.cumulativeProbability(x) - kernel.cumulativeProbability(lower)) / kB;
658 return pBminus + pB * withinBinCum;
659 }
660
661 /**
662 * {@inheritDoc}
663 *
664 * <p>Algorithm description:<ol>
665 * <li>Find the smallest i such that the sum of the masses of the bins
666 * through i is at least p.</li>
667 * <li>
668 * Let K be the within-bin kernel distribution for bin i.</br>
669 * Let K(B) be the mass of B under K. <br/>
670 * Let K(B-) be K evaluated at the lower endpoint of B (the combined
671 * mass of the bins below B under K).<br/>
672 * Let P(B) be the probability of bin i.<br/>
673 * Let P(B-) be the sum of the bin masses below bin i. <br/>
674 * Let pCrit = p - P(B-)<br/>
675 * <li>Return the inverse of K evaluated at <br/>
676 * K(B-) + pCrit * K(B) / P(B) </li>
677 * </ol></p>
678 *
679 * @since 3.1
680 */
681 @Override
682 public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
683 if (p < 0.0 || p > 1.0) {
684 throw new OutOfRangeException(p, 0, 1);
685 }
686
687 if (p == 0.0) {
688 return getSupportLowerBound();
689 }
690
691 if (p == 1.0) {
692 return getSupportUpperBound();
693 }
694
695 int i = 0;
696 while (cumBinP(i) < p) {
697 i++;
698 }
699
700 final RealDistribution kernel = getKernel(binStats.get(i));
701 final double kB = kB(i);
702 final double[] binBounds = getUpperBounds();
703 final double lower = i == 0 ? min : binBounds[i - 1];
704 final double kBminus = kernel.cumulativeProbability(lower);
705 final double pB = pB(i);
706 final double pBminus = pBminus(i);
707 final double pCrit = p - pBminus;
708 if (pCrit <= 0) {
709 return lower;
710 }
711 return kernel.inverseCumulativeProbability(kBminus + pCrit * kB / pB);
712 }
713
714 /**
715 * {@inheritDoc}
716 * @since 3.1
717 */
718 public double getNumericalMean() {
719 return sampleStats.getMean();
720 }
721
722 /**
723 * {@inheritDoc}
724 * @since 3.1
725 */
726 public double getNumericalVariance() {
727 return sampleStats.getVariance();
728 }
729
730 /**
731 * {@inheritDoc}
732 * @since 3.1
733 */
734 public double getSupportLowerBound() {
735 return min;
736 }
737
738 /**
739 * {@inheritDoc}
740 * @since 3.1
741 */
742 public double getSupportUpperBound() {
743 return max;
744 }
745
746 /**
747 * {@inheritDoc}
748 * @since 3.1
749 */
750 public boolean isSupportLowerBoundInclusive() {
751 return true;
752 }
753
754 /**
755 * {@inheritDoc}
756 * @since 3.1
757 */
758 public boolean isSupportUpperBoundInclusive() {
759 return true;
760 }
761
762 /**
763 * {@inheritDoc}
764 * @since 3.1
765 */
766 public boolean isSupportConnected() {
767 return true;
768 }
769
770 /**
771 * {@inheritDoc}
772 * @since 3.1
773 */
774 @Override
775 public void reseedRandomGenerator(long seed) {
776 randomData.reSeed(seed);
777 }
778
779 /**
780 * The probability of bin i.
781 *
782 * @param i the index of the bin
783 * @return the probability that selection begins in bin i
784 */
785 private double pB(int i) {
786 return i == 0 ? upperBounds[0] :
787 upperBounds[i] - upperBounds[i - 1];
788 }
789
790 /**
791 * The combined probability of the bins up to but not including bin i.
792 *
793 * @param i the index of the bin
794 * @return the probability that selection begins in a bin below bin i.
795 */
796 private double pBminus(int i) {
797 return i == 0 ? 0 : upperBounds[i - 1];
798 }
799
800 /**
801 * Mass of bin i under the within-bin kernel of the bin.
802 *
803 * @param i index of the bin
804 * @return the difference in the within-bin kernel cdf between the
805 * upper and lower endpoints of bin i
806 */
807 @SuppressWarnings("deprecation")
808 private double kB(int i) {
809 final double[] binBounds = getUpperBounds();
810 final RealDistribution kernel = getKernel(binStats.get(i));
811 return i == 0 ? kernel.cumulativeProbability(min, binBounds[0]) :
812 kernel.cumulativeProbability(binBounds[i - 1], binBounds[i]);
813 }
814
815 /**
816 * The within-bin kernel of the bin that x belongs to.
817 *
818 * @param x the value to locate within a bin
819 * @return the within-bin kernel of the bin containing x
820 */
821 private RealDistribution k(double x) {
822 final int binIndex = findBin(x);
823 return getKernel(binStats.get(binIndex));
824 }
825
826 /**
827 * The combined probability of the bins up to and including binIndex.
828 *
829 * @param binIndex maximum bin index
830 * @return sum of the probabilities of bins through binIndex
831 */
832 private double cumBinP(int binIndex) {
833 return upperBounds[binIndex];
834 }
835
836 /**
837 * The within-bin smoothing kernel. Returns a Gaussian distribution
838 * parameterized by {@code bStats}, unless the bin contains only one
839 * observation, in which case a constant distribution is returned.
840 *
841 * @param bStats summary statistics for the bin
842 * @return within-bin kernel parameterized by bStats
843 */
844 protected RealDistribution getKernel(SummaryStatistics bStats) {
845 if (bStats.getN() == 1 || bStats.getVariance() == 0) {
846 return new ConstantRealDistribution(bStats.getMean());
847 } else {
848 return new NormalDistribution(randomData.getRandomGenerator(),
849 bStats.getMean(), bStats.getStandardDeviation(),
850 NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
851 }
852 }
853}
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