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The Hipparchus statistics module
/*
* 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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.stat.fitting;
import java.io.BufferedReader;
import java.io.File;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.URL;
import java.nio.charset.Charset;
import java.nio.file.Files;
import java.util.ArrayList;
import java.util.List;
import org.hipparchus.distribution.RealDistribution;
import org.hipparchus.distribution.continuous.AbstractRealDistribution;
import org.hipparchus.distribution.continuous.ConstantRealDistribution;
import org.hipparchus.distribution.continuous.NormalDistribution;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.exception.MathRuntimeException;
import org.hipparchus.exception.NullArgumentException;
import org.hipparchus.random.RandomDataGenerator;
import org.hipparchus.random.RandomGenerator;
import org.hipparchus.stat.descriptive.StatisticalSummary;
import org.hipparchus.stat.descriptive.StreamingStatistics;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathUtils;
/**
* Represents an
* empirical probability distribution -- a probability distribution derived
* from observed data without making any assumptions about the functional form
* of the population distribution that the data come from.
*
* An EmpiricalDistribution maintains data structures, called
* distribution digests, that describe empirical distributions and
* support the following operations:
* - loading the distribution from a file of observed data values
* - dividing the input data into "bin ranges" and reporting bin frequency
* counts (data for histogram)
* - reporting univariate statistics describing the full set of data values
* as well as the observations within each bin
* - generating random values from the distribution
*
* Applications can use EmpiricalDistribution 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.
*
* The implementation uses what amounts to the
*
* Variable Kernel Method with Gaussian smoothing:
* Digesting the input file
*
- Pass the file once to compute min and max.
* - Divide the range from min-max into
binCount "bins."
* - Pass the data file again, computing bin counts and univariate
* statistics (mean, std dev.) for each of the bins
* - Divide the interval (0,1) into subintervals associated with the bins,
* with the length of a bin's subinterval proportional to its count.
* Generating random values from the distribution
* - Generate a uniformly distributed value in (0,1)
* - Select the subinterval to which the value belongs.
*
- Generate a random Gaussian value with mean = mean of the associated
* bin and std dev = std dev of associated bin.
*
* 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.
*
*USAGE NOTES:
*- The
binCount 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.
*- The input file must be a plain text file containing one valid numeric
* entry per line.
*
*
*/
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 binStats;
/** Sample statistics */
private StreamingStatistics sampleStats;
/** Max loaded value */
private double max = Double.NEGATIVE_INFINITY;
/** Min loaded value */
private double min = Double.POSITIVE_INFINITY;
/** Grid size */
private double delta;
/** number of bins */
private final int binCount;
/** is the distribution loaded? */
private boolean loaded;
/** upper bounds of subintervals in (0,1) "belonging" to the bins */
private double[] upperBounds;
/**
* 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 MathIllegalArgumentException 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 MathIllegalArgumentException if {@code binCount <= 0}.
*/
public EmpiricalDistribution(int binCount, RandomGenerator generator) {
this(binCount, RandomDataGenerator.of(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)
*/
public EmpiricalDistribution(RandomGenerator generator) {
this(DEFAULT_BIN_COUNT, generator);
}
/**
* 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 MathIllegalArgumentException if {@code binCount <= 0}.
*/
private EmpiricalDistribution(int binCount,
RandomDataGenerator randomData) {
if (binCount <= 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL_BOUND_EXCLUDED,
binCount, 0);
}
this.binCount = binCount;
this.randomData = randomData;
binStats = new ArrayList<>();
}
/**
* 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 MathRuntimeException.createInternalError();
}
loaded = true;
}
/**
* Computes the empirical distribution using data read from a URL.
*
* The input file must 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 MathIllegalArgumentException if URL contains no data
*/
public void load(URL url) throws IOException, MathIllegalArgumentException, NullArgumentException {
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 MathIllegalArgumentException(LocalizedCoreFormats.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.
*
* The input file must 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);
try (InputStream is1 = Files.newInputStream(file.toPath());
BufferedReader in1 = new BufferedReader(new InputStreamReader(is1, charset))) {
DataAdapter da = new StreamDataAdapter(in1);
da.computeStats();
// new adapter for second pass
try (InputStream is2 = Files.newInputStream(file.toPath());
BufferedReader in2 = new BufferedReader(new InputStreamReader(is2, charset))) {
fillBinStats(new StreamDataAdapter(in2));
}
loaded = true;
}
}
/**
* Provides methods for computing sampleStats and
* beanStats 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;
}
/**
* DataAdapter 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 {
double val = 0.0d;
for (String str = inputStream.readLine(); str != null; str = inputStream.readLine()) {
val = Double.parseDouble(str);
StreamingStatistics stats = binStats.get(findBin(val));
stats.addValue(val);
}
inputStream.close();
inputStream = null;
}
/** {@inheritDoc} */
@Override
public void computeStats() throws IOException {
double val = 0.0;
sampleStats = new StreamingStatistics();
for (String str = inputStream.readLine(); str != null; str = inputStream.readLine()) {
val = Double.parseDouble(str);
sampleStats.addValue(val);
}
inputStream.close();
inputStream = null;
}
}
/**
* DataAdapter for data provided as array of doubles.
*/
private class ArrayDataAdapter extends DataAdapter {
/** Array of input data values */
private final double[] inputArray;
/**
* Construct an ArrayDataAdapter from a double[] array
*
* @param in double[] array holding the data, a reference to the array will be stored
* @throws NullArgumentException if in is null
*/
ArrayDataAdapter(double[] in) throws NullArgumentException { // NOPMD - storing a reference to the array is intentional and documented here
super();
MathUtils.checkNotNull(in);
inputArray = in;
}
/** {@inheritDoc} */
@Override
public void computeStats() throws IOException {
sampleStats = new StreamingStatistics();
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++) {
StreamingStatistics 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)/binCount;
// Initialize binStats ArrayList
if (!binStats.isEmpty()) {
binStats.clear();
}
for (int i = 0; i < binCount; i++) {
StreamingStatistics stats = new StreamingStatistics();
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.
* Preconditions:
* - the distribution must be loaded before invoking this method
* @return the random value.
* @throws MathIllegalStateException if the distribution has not been loaded
*/
public double getNextValue() throws MathIllegalStateException {
if (!loaded) {
throw new MathIllegalStateException(LocalizedCoreFormats.DISTRIBUTION_NOT_LOADED);
}
return inverseCumulativeProbability(randomData.nextDouble());
}
/**
* Returns a {@link StatisticalSummary} describing this distribution.
* Preconditions:
* - the distribution must be loaded before invoking this method
*
* @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 StreamingStatistics} 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 getBinStats() {
return binStats;
}
/**
* Returns a fresh copy of the array of upper bounds for the bins.
* Bins are:
* [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],...,
* (upperBounds[binCount-2], upperBounds[binCount-1] = max].
*
* @return array of bin upper bounds
*/
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.
*
* Preconditions:
* - the distribution must be loaded before invoking this method
*
* @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
*/
public void reSeed(long seed) {
randomData.setSeed(seed);
}
// Distribution methods ---------------------------
/**
* {@inheritDoc}
*
* Returns the kernel density normalized so that its integral over each bin
* equals the bin mass.
*
* Algorithm description:
* - Find the bin B that x belongs to.
* - Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the
* integral of the kernel density over B).
* - Return k(x) * P(B) / K(B), where k is the within-bin kernel density
* and P(B) is the mass of B.
*/
@Override
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}
*
* Algorithm description:
* - Find the bin B that x belongs to.
* - Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B.
* - 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
* - Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where
* K(x) is the within-bin kernel distribution function evaluated at x.
* If K is a constant distribution, we return P(B-) + P(B) (counting the full
* mass of B).
*
*/
@Override
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}
*
* Algorithm description:
* - Find the smallest i such that the sum of the masses of the bins
* through i is at least p.
* -
* Let K be the within-bin kernel distribution for bin i.
* Let K(B) be the mass of B under K.
* Let K(B-) be K evaluated at the lower endpoint of B (the combined
* mass of the bins below B under K).
* Let P(B) be the probability of bin i.
* Let P(B-) be the sum of the bin masses below bin i.
* Let pCrit = p - P(B-)
* - Return the inverse of K evaluated at
* K(B-) + pCrit * K(B) / P(B)
*
*
*/
@Override
public double inverseCumulativeProbability(final double p) throws MathIllegalArgumentException {
MathUtils.checkRangeInclusive(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}
*/
@Override
public double getNumericalMean() {
return sampleStats.getMean();
}
/**
* {@inheritDoc}
*/
@Override
public double getNumericalVariance() {
return sampleStats.getVariance();
}
/**
* {@inheritDoc}
*/
@Override
public double getSupportLowerBound() {
return min;
}
/**
* {@inheritDoc}
*/
@Override
public double getSupportUpperBound() {
return max;
}
/**
* {@inheritDoc}
*/
@Override
public boolean isSupportConnected() {
return true;
}
/**
* Reseed the underlying PRNG.
*
* @param seed new seed value
*/
public void reseedRandomGenerator(long seed) {
randomData.setSeed(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
*/
private double kB(int i) {
final double[] binBounds = getUpperBounds();
final RealDistribution kernel = getKernel(binStats.get(i));
return i == 0 ? kernel.probability(min, binBounds[0]) :
kernel.probability(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 less than 2
* observations, 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(StreamingStatistics bStats) {
if (bStats.getN() < 2 || bStats.getVariance() == 0) {
return new ConstantRealDistribution(bStats.getMean());
} else {
return new NormalDistribution(bStats.getMean(),
bStats.getStandardDeviation());
}
}
}