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 */ 017 018 package org.apache.commons.math3.random; 019 020 import java.io.BufferedReader; 021 import java.io.File; 022 import java.io.FileInputStream; 023 import java.io.IOException; 024 import java.io.InputStream; 025 import java.io.InputStreamReader; 026 import java.net.URL; 027 import java.nio.charset.Charset; 028 import java.util.ArrayList; 029 import java.util.List; 030 031 import org.apache.commons.math3.distribution.AbstractRealDistribution; 032 import org.apache.commons.math3.distribution.NormalDistribution; 033 import org.apache.commons.math3.distribution.RealDistribution; 034 import org.apache.commons.math3.exception.MathIllegalStateException; 035 import org.apache.commons.math3.exception.MathInternalError; 036 import org.apache.commons.math3.exception.NullArgumentException; 037 import org.apache.commons.math3.exception.OutOfRangeException; 038 import org.apache.commons.math3.exception.ZeroException; 039 import org.apache.commons.math3.exception.util.LocalizedFormats; 040 import org.apache.commons.math3.stat.descriptive.StatisticalSummary; 041 import org.apache.commons.math3.stat.descriptive.SummaryStatistics; 042 import org.apache.commons.math3.util.FastMath; 043 import org.apache.commons.math3.util.MathUtils; 044 045 /** 046 * <p>Represents an <a href="http://http://en.wikipedia.org/wiki/Empirical_distribution_function"> 047 * empirical probability distribution</a> -- a probability distribution derived 048 * from observed data without making any assumptions about the functional form 049 * of the population distribution that the data come from.</p> 050 * 051 * <p>An <code>EmpiricalDistribution</code> maintains data structures, called 052 * <i>distribution digests</i>, that describe empirical distributions and 053 * support the following operations: <ul> 054 * <li>loading the distribution from a file of observed data values</li> 055 * <li>dividing the input data into "bin ranges" and reporting bin frequency 056 * counts (data for histogram)</li> 057 * <li>reporting univariate statistics describing the full set of data values 058 * as well as the observations within each bin</li> 059 * <li>generating random values from the distribution</li> 060 * </ul> 061 * Applications can use <code>EmpiricalDistribution</code> to build grouped 062 * frequency histograms representing the input data or to generate random values 063 * "like" those in the input file -- i.e., the values generated will follow the 064 * distribution of the values in the file.</p> 065 * 066 * <p>The implementation uses what amounts to the 067 * <a href="http://nedwww.ipac.caltech.edu/level5/March02/Silverman/Silver2_6.html"> 068 * Variable Kernel Method</a> with Gaussian smoothing:<p> 069 * <strong>Digesting the input file</strong> 070 * <ol><li>Pass the file once to compute min and max.</li> 071 * <li>Divide the range from min-max into <code>binCount</code> "bins."</li> 072 * <li>Pass the data file again, computing bin counts and univariate 073 * statistics (mean, std dev.) for each of the bins </li> 074 * <li>Divide the interval (0,1) into subintervals associated with the bins, 075 * with the length of a bin's subinterval proportional to its count.</li></ol> 076 * <strong>Generating random values from the distribution</strong><ol> 077 * <li>Generate a uniformly distributed value in (0,1) </li> 078 * <li>Select the subinterval to which the value belongs. 079 * <li>Generate a random Gaussian value with mean = mean of the associated 080 * bin and std dev = std dev of associated bin.</li></ol></p> 081 * 082 * <p>EmpiricalDistribution implements the {@link RealDistribution} interface 083 * as follows. Given x within the range of values in the dataset, let B 084 * be the bin containing x and let K be the within-bin kernel for B. Let P(B-) 085 * be the sum of the probabilities of the bins below B and let K(B) be the 086 * mass of B under K (i.e., the integral of the kernel density over B). Then 087 * set P(X < x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution 088 * evaluated at x. This results in a cdf that matches the grouped frequency 089 * distribution at the bin endpoints and interpolates within bins using 090 * within-bin kernels.</p> 091 * 092 *<strong>USAGE NOTES:</strong><ul> 093 *<li>The <code>binCount</code> is set by default to 1000. A good rule of thumb 094 * is to set the bin count to approximately the length of the input file divided 095 * by 10. </li> 096 *<li>The input file <i>must</i> be a plain text file containing one valid numeric 097 * entry per line.</li> 098 * </ul></p> 099 * 100 * @version $Id: EmpiricalDistribution.java 1422350 2012-12-15 20:47:47Z psteitz $ 101 */ 102 public 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 /** List of SummaryStatistics objects characterizing the bins */ 114 private final List<SummaryStatistics> binStats; 115 116 /** Sample statistics */ 117 private SummaryStatistics sampleStats = null; 118 119 /** Max loaded value */ 120 private double max = Double.NEGATIVE_INFINITY; 121 122 /** Min loaded value */ 123 private double min = Double.POSITIVE_INFINITY; 124 125 /** Grid size */ 126 private double delta = 0d; 127 128 /** number of bins */ 129 private final int binCount; 130 131 /** is the distribution loaded? */ 132 private boolean loaded = false; 133 134 /** upper bounds of subintervals in (0,1) "belonging" to the bins */ 135 private double[] upperBounds = null; 136 137 /** RandomDataGenerator instance to use in repeated calls to getNext() */ 138 private final RandomDataGenerator randomData; 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(null); 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.valueOf(str).doubleValue(); 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.valueOf(binCount)).doubleValue(); 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 // Start with a uniformly distributed random number in (0,1) 482 final double x = randomData.nextUniform(0,1); 483 484 // Use this to select the bin and generate a Gaussian within the bin 485 for (int i = 0; i < binCount; i++) { 486 if (x <= upperBounds[i]) { 487 SummaryStatistics stats = binStats.get(i); 488 if (stats.getN() > 0) { 489 if (stats.getStandardDeviation() > 0) { // more than one obs 490 return randomData.nextGaussian(stats.getMean(), 491 stats.getStandardDeviation()); 492 } else { 493 return stats.getMean(); // only one obs in bin 494 } 495 } 496 } 497 } 498 throw new MathIllegalStateException(LocalizedFormats.NO_BIN_SELECTED); 499 } 500 501 /** 502 * Returns a {@link StatisticalSummary} describing this distribution. 503 * <strong>Preconditions:</strong><ul> 504 * <li>the distribution must be loaded before invoking this method</li></ul> 505 * 506 * @return the sample statistics 507 * @throws IllegalStateException if the distribution has not been loaded 508 */ 509 public StatisticalSummary getSampleStats() { 510 return sampleStats; 511 } 512 513 /** 514 * Returns the number of bins. 515 * 516 * @return the number of bins. 517 */ 518 public int getBinCount() { 519 return binCount; 520 } 521 522 /** 523 * Returns a List of {@link SummaryStatistics} instances containing 524 * statistics describing the values in each of the bins. The list is 525 * indexed on the bin number. 526 * 527 * @return List of bin statistics. 528 */ 529 public List<SummaryStatistics> getBinStats() { 530 return binStats; 531 } 532 533 /** 534 * <p>Returns a fresh copy of the array of upper bounds for the bins. 535 * Bins are: <br/> 536 * [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],..., 537 * (upperBounds[binCount-2], upperBounds[binCount-1] = max].</p> 538 * 539 * <p>Note: In versions 1.0-2.0 of commons-math, this method 540 * incorrectly returned the array of probability generator upper 541 * bounds now returned by {@link #getGeneratorUpperBounds()}.</p> 542 * 543 * @return array of bin upper bounds 544 * @since 2.1 545 */ 546 public double[] getUpperBounds() { 547 double[] binUpperBounds = new double[binCount]; 548 for (int i = 0; i < binCount - 1; i++) { 549 binUpperBounds[i] = min + delta * (i + 1); 550 } 551 binUpperBounds[binCount - 1] = max; 552 return binUpperBounds; 553 } 554 555 /** 556 * <p>Returns a fresh copy of the array of upper bounds of the subintervals 557 * of [0,1] used in generating data from the empirical distribution. 558 * Subintervals correspond to bins with lengths proportional to bin counts.</p> 559 * 560 * <p>In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned 561 * by {@link #getUpperBounds()}.</p> 562 * 563 * @since 2.1 564 * @return array of upper bounds of subintervals used in data generation 565 */ 566 public double[] getGeneratorUpperBounds() { 567 int len = upperBounds.length; 568 double[] out = new double[len]; 569 System.arraycopy(upperBounds, 0, out, 0, len); 570 return out; 571 } 572 573 /** 574 * Property indicating whether or not the distribution has been loaded. 575 * 576 * @return true if the distribution has been loaded 577 */ 578 public boolean isLoaded() { 579 return loaded; 580 } 581 582 /** 583 * Reseeds the random number generator used by {@link #getNextValue()}. 584 * 585 * @param seed random generator seed 586 * @since 3.0 587 */ 588 public void reSeed(long seed) { 589 randomData.reSeed(seed); 590 } 591 592 // Distribution methods --------------------------- 593 594 /** 595 * {@inheritDoc} 596 * @since 3.1 597 */ 598 public double probability(double x) { 599 return 0; 600 } 601 602 /** 603 * {@inheritDoc} 604 * 605 * <p>Returns the kernel density normalized so that its integral over each bin 606 * equals the bin mass.</p> 607 * 608 * <p>Algorithm description: <ol> 609 * <li>Find the bin B that x belongs to.</li> 610 * <li>Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the 611 * integral of the kernel density over B).</li> 612 * <li>Return k(x) * P(B) / K(B), where k is the within-bin kernel density 613 * and P(B) is the mass of B.</li></ol></p> 614 * @since 3.1 615 */ 616 public double density(double x) { 617 if (x < min || x > max) { 618 return 0d; 619 } 620 final int binIndex = findBin(x); 621 final RealDistribution kernel = getKernel(binStats.get(binIndex)); 622 return kernel.density(x) * pB(binIndex) / kB(binIndex); 623 } 624 625 /** 626 * {@inheritDoc} 627 * 628 * <p>Algorithm description:<ol> 629 * <li>Find the bin B that x belongs to.</li> 630 * <li>Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B.</li> 631 * <li>Compute K(B) = the probability mass of B with respect to the within-bin kernel 632 * and K(B-) = the kernel distribution evaluated at the lower endpoint of B</li> 633 * <li>Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where 634 * K(x) is the within-bin kernel distribution function evaluated at x.</li></ol></p> 635 * 636 * @since 3.1 637 */ 638 public double cumulativeProbability(double x) { 639 if (x < min) { 640 return 0d; 641 } else if (x >= max) { 642 return 1d; 643 } 644 final int binIndex = findBin(x); 645 final double pBminus = pBminus(binIndex); 646 final double pB = pB(binIndex); 647 final double[] binBounds = getUpperBounds(); 648 final double kB = kB(binIndex); 649 final double lower = binIndex == 0 ? min : binBounds[binIndex - 1]; 650 final RealDistribution kernel = k(x); 651 final double withinBinCum = 652 (kernel.cumulativeProbability(x) - kernel.cumulativeProbability(lower)) / kB; 653 return pBminus + pB * withinBinCum; 654 } 655 656 /** 657 * {@inheritDoc} 658 * 659 * <p>Algorithm description:<ol> 660 * <li>Find the smallest i such that the sum of the masses of the bins 661 * through i is at least p.</li> 662 * <li> 663 * Let K be the within-bin kernel distribution for bin i.</br> 664 * Let K(B) be the mass of B under K. <br/> 665 * Let K(B-) be K evaluated at the lower endpoint of B (the combined 666 * mass of the bins below B under K).<br/> 667 * Let P(B) be the probability of bin i.<br/> 668 * Let P(B-) be the sum of the bin masses below bin i. <br/> 669 * Let pCrit = p - P(B-)<br/> 670 * <li>Return the inverse of K evaluated at <br/> 671 * K(B-) + pCrit * K(B) / P(B) </li> 672 * </ol></p> 673 * 674 * @since 3.1 675 */ 676 public double inverseCumulativeProbability(final double p) throws OutOfRangeException { 677 if (p < 0.0 || p > 1.0) { 678 throw new OutOfRangeException(p, 0, 1); 679 } 680 681 if (p == 0.0) { 682 return getSupportLowerBound(); 683 } 684 685 if (p == 1.0) { 686 return getSupportUpperBound(); 687 } 688 689 int i = 0; 690 while (cumBinP(i) < p) { 691 i++; 692 } 693 694 final RealDistribution kernel = getKernel(binStats.get(i)); 695 final double kB = kB(i); 696 final double[] binBounds = getUpperBounds(); 697 final double lower = i == 0 ? min : binBounds[i - 1]; 698 final double kBminus = kernel.cumulativeProbability(lower); 699 final double pB = pB(i); 700 final double pBminus = pBminus(i); 701 final double pCrit = p - pBminus; 702 if (pCrit <= 0) { 703 return lower; 704 } 705 return kernel.inverseCumulativeProbability(kBminus + pCrit * kB / pB); 706 } 707 708 /** 709 * {@inheritDoc} 710 * @since 3.1 711 */ 712 public double getNumericalMean() { 713 return sampleStats.getMean(); 714 } 715 716 /** 717 * {@inheritDoc} 718 * @since 3.1 719 */ 720 public double getNumericalVariance() { 721 return sampleStats.getVariance(); 722 } 723 724 /** 725 * {@inheritDoc} 726 * @since 3.1 727 */ 728 public double getSupportLowerBound() { 729 return min; 730 } 731 732 /** 733 * {@inheritDoc} 734 * @since 3.1 735 */ 736 public double getSupportUpperBound() { 737 return max; 738 } 739 740 /** 741 * {@inheritDoc} 742 * @since 3.1 743 */ 744 public boolean isSupportLowerBoundInclusive() { 745 return true; 746 } 747 748 /** 749 * {@inheritDoc} 750 * @since 3.1 751 */ 752 public boolean isSupportUpperBoundInclusive() { 753 return true; 754 } 755 756 /** 757 * {@inheritDoc} 758 * @since 3.1 759 */ 760 public boolean isSupportConnected() { 761 return true; 762 } 763 764 /** 765 * {@inheritDoc} 766 * @since 3.1 767 */ 768 @Override 769 public double sample() { 770 return getNextValue(); 771 } 772 773 /** 774 * {@inheritDoc} 775 * @since 3.1 776 */ 777 @Override 778 public void reseedRandomGenerator(long seed) { 779 randomData.reSeed(seed); 780 } 781 782 /** 783 * The probability of bin i. 784 * 785 * @param i the index of the bin 786 * @return the probability that selection begins in bin i 787 */ 788 private double pB(int i) { 789 return i == 0 ? upperBounds[0] : 790 upperBounds[i] - upperBounds[i - 1]; 791 } 792 793 /** 794 * The combined probability of the bins up to but not including bin i. 795 * 796 * @param i the index of the bin 797 * @return the probability that selection begins in a bin below bin i. 798 */ 799 private double pBminus(int i) { 800 return i == 0 ? 0 : upperBounds[i - 1]; 801 } 802 803 /** 804 * Mass of bin i under the within-bin kernel of the bin. 805 * 806 * @param i index of the bin 807 * @return the difference in the within-bin kernel cdf between the 808 * upper and lower endpoints of bin i 809 */ 810 @SuppressWarnings("deprecation") 811 private double kB(int i) { 812 final double[] binBounds = getUpperBounds(); 813 final RealDistribution kernel = getKernel(binStats.get(i)); 814 return i == 0 ? kernel.cumulativeProbability(min, binBounds[0]) : 815 kernel.cumulativeProbability(binBounds[i - 1], binBounds[i]); 816 } 817 818 /** 819 * The within-bin kernel of the bin that x belongs to. 820 * 821 * @param x the value to locate within a bin 822 * @return the within-bin kernel of the bin containing x 823 */ 824 private RealDistribution k(double x) { 825 final int binIndex = findBin(x); 826 return getKernel(binStats.get(binIndex)); 827 } 828 829 /** 830 * The combined probability of the bins up to and including binIndex. 831 * 832 * @param binIndex maximum bin index 833 * @return sum of the probabilities of bins through binIndex 834 */ 835 private double cumBinP(int binIndex) { 836 return upperBounds[binIndex]; 837 } 838 839 /** 840 * The within-bin smoothing kernel. 841 * 842 * @param bStats summary statistics for the bin 843 * @return within-bin kernel parameterized by bStats 844 */ 845 private RealDistribution getKernel(SummaryStatistics bStats) { 846 // For now, hard-code Gaussian (only kernel supported) 847 return new NormalDistribution( 848 bStats.getMean(), bStats.getStandardDeviation()); 849 } 850 }