/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.random;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.URL;
import java.nio.charset.Charset;
import java.util.ArrayList;
import java.util.List;

import org.apache.commons.math3.distribution.AbstractRealDistribution;
import org.apache.commons.math3.distribution.ConstantRealDistribution;
import org.apache.commons.math3.distribution.NormalDistribution;
import org.apache.commons.math3.distribution.RealDistribution;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.stat.descriptive.StatisticalSummary;
import org.apache.commons.math3.stat.descriptive.SummaryStatistics;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;

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 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.

/**
 * <p>Represents an <a href="http://http://en.wikipedia.org/wiki/Empirical_distribution_function">
 * empirical probability distribution</a> -- a probability distribution derived
 * from observed data without making any assumptions about the functional form
 * of the population distribution that the data come from.</p>
 *
 * <p>An <code>EmpiricalDistribution</code> maintains data structures, called
 * <i>distribution digests</i>, that describe empirical distributions and
 * support the following operations: <ul>
 * <li>loading the distribution from a file of observed data values</li>
 * <li>dividing the input data into "bin ranges" and reporting bin frequency
 *     counts (data for histogram)</li>
 * <li>reporting univariate statistics describing the full set of data values
 *     as well as the observations within each bin</li>
 * <li>generating random values from the distribution</li>
 * </ul>
 * Applications can use <code>EmpiricalDistribution</code> to build grouped
 * frequency histograms representing the input data or to generate random values
 * "like" those in the input file -- i.e., the values generated will follow the
 * distribution of the values in the file.</p>
 *
 * <p>The implementation uses what amounts to the
 * <a href="http://nedwww.ipac.caltech.edu/level5/March02/Silverman/Silver2_6.html">
 * Variable Kernel Method</a> with Gaussian smoothing:<p>
 * <strong>Digesting the input file</strong>
 * <ol><li>Pass the file once to compute min and max.</li>
 * <li>Divide the range from min-max into <code>binCount</code> "bins."</li>
 * <li>Pass the data file again, computing bin counts and univariate
 *     statistics (mean, std dev.) for each of the bins </li>
 * <li>Divide the interval (0,1) into subintervals associated with the bins,
 *     with the length of a bin's subinterval proportional to its count.</li></ol>
 * <strong>Generating random values from the distribution</strong><ol>
 * <li>Generate a uniformly distributed value in (0,1) </li>
 * <li>Select the subinterval to which the value belongs.
 * <li>Generate a random Gaussian value with mean = mean of the associated
 *     bin and std dev = std dev of associated bin.</li></ol></p>
 *
 * <p>EmpiricalDistribution implements the {@link RealDistribution} interface
 * as follows.  Given x within the range of values in the dataset, let B
 * be the bin containing x and let K be the within-bin kernel for B.  Let P(B-)
 * be the sum of the probabilities of the bins below B and let K(B) be the
 * mass of B under K (i.e., the integral of the kernel density over B).  Then
 * set P(X < x) = P(B-) + P(B) * K(x) / K(B) where K(x) is the kernel distribution
 * evaluated at x. This results in a cdf that matches the grouped frequency
 * distribution at the bin endpoints and interpolates within bins using
 * within-bin kernels.</p>
 *
 *<strong>USAGE NOTES:</strong><ul>
 *<li>The <code>binCount</code> is set by default to 1000.  A good rule of thumb
 *    is to set the bin count to approximately the length of the input file divided
 *    by 10. </li>
 *<li>The input file <i>must</i> be a plain text file containing one valid numeric
 *    entry per line.</li>
 * </ul></p>
 *
 */
public class EmpiricalDistribution extends AbstractRealDistribution {

    
Default bin count /** Default bin count */
    public static final int DEFAULT_BIN_COUNT = 1000;

    
Character set for file input /** Character set for file input */
    private static final String FILE_CHARSET = "US-ASCII";

    
Serializable version identifier /** Serializable version identifier */
    private static final long serialVersionUID = 5729073523949762654L;

    
RandomDataGenerator instance to use in repeated calls to getNext() /** RandomDataGenerator instance to use in repeated calls to getNext() */
    protected final RandomDataGenerator randomData;

    
List of SummaryStatistics objects characterizing the bins /** List of SummaryStatistics objects characterizing the bins */
    private final List<SummaryStatistics> binStats;

    
Sample statistics /** Sample statistics */
    private SummaryStatistics sampleStats = null;

    
Max loaded value /** Max loaded value */
    private double max = Double.NEGATIVE_INFINITY;

    
Min loaded value /** Min loaded value */
    private double min = Double.POSITIVE_INFINITY;

    
Grid size /** Grid size */
    private double delta = 0d;

    
number of bins /** number of bins */
    private final int binCount;

    
is the distribution loaded? /** is the distribution loaded? */
    private boolean loaded = false;

    
upper bounds of subintervals in (0,1) "belonging" to the bins /** upper bounds of subintervals in (0,1) "belonging" to the bins */
    private double[] upperBounds = null;

    
Creates a new EmpiricalDistribution with the default bin count.
/**
     * Creates a new EmpiricalDistribution with the default bin count.
     */
    public EmpiricalDistribution() {
        this(DEFAULT_BIN_COUNT);
    }

    
Creates a new EmpiricalDistribution with the specified bin count.
Params:
binCount – number of bins. Must be strictly positive.
Throws:
NotStrictlyPositiveException – if binCount <= 0./**
     * Creates a new EmpiricalDistribution with the specified bin count.
     *
     * @param binCount number of bins. Must be strictly positive.
     * @throws NotStrictlyPositiveException if {@code binCount <= 0}.
     */
    public EmpiricalDistribution(int binCount) {
        this(binCount, new RandomDataGenerator());
    }

    
Creates a new EmpiricalDistribution with the specified bin count using the provided RandomGenerator as the source of random data. 
Params:
binCount – number of bins. Must be strictly positive.
generator – random data generator (may be null, resulting in default JDK generator)
Throws:
NotStrictlyPositiveException – if binCount <= 0.
Since:
3.0/**
     * Creates a new EmpiricalDistribution with the specified bin count using the
     * provided {@link RandomGenerator} as the source of random data.
     *
     * @param binCount number of bins. Must be strictly positive.
     * @param generator random data generator (may be null, resulting in default JDK generator)
     * @throws NotStrictlyPositiveException if {@code binCount <= 0}.
     * @since 3.0
     */
    public EmpiricalDistribution(int binCount, RandomGenerator generator) {
        this(binCount, new RandomDataGenerator(generator));
    }

    
Creates a new EmpiricalDistribution with default bin count using the provided RandomGenerator as the source of random data. 
Params:
generator – random data generator (may be null, resulting in default JDK generator)
Since:
3.0/**
     * Creates a new EmpiricalDistribution with default bin count using the
     * provided {@link RandomGenerator} as the source of random data.
     *
     * @param generator random data generator (may be null, resulting in default JDK generator)
     * @since 3.0
     */
    public EmpiricalDistribution(RandomGenerator generator) {
        this(DEFAULT_BIN_COUNT, generator);
    }

    
Creates a new EmpiricalDistribution with the specified bin count using the provided RandomDataImpl instance as the source of random data. 
Params:
binCount – number of bins
randomData – random data generator (may be null, resulting in default JDK generator)
Since:
3.0
Deprecated:
As of 3.1. Please use EmpiricalDistribution(int, RandomGenerator) instead./**
     * Creates a new EmpiricalDistribution with the specified bin count using the
     * provided {@link RandomDataImpl} instance as the source of random data.
     *
     * @param binCount number of bins
     * @param randomData random data generator (may be null, resulting in default JDK generator)
     * @since 3.0
     * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(int,RandomGenerator)} instead.
     */
    @Deprecated
    public EmpiricalDistribution(int binCount, RandomDataImpl randomData) {
        this(binCount, randomData.getDelegate());
    }

    
Creates a new EmpiricalDistribution with default bin count using the provided RandomDataImpl as the source of random data. 
Params:
randomData – random data generator (may be null, resulting in default JDK generator)
Since:
3.0
Deprecated:
As of 3.1. Please use EmpiricalDistribution(RandomGenerator) instead./**
     * Creates a new EmpiricalDistribution with default bin count using the
     * provided {@link RandomDataImpl} as the source of random data.
     *
     * @param randomData random data generator (may be null, resulting in default JDK generator)
     * @since 3.0
     * @deprecated As of 3.1. Please use {@link #EmpiricalDistribution(RandomGenerator)} instead.
     */
    @Deprecated
    public EmpiricalDistribution(RandomDataImpl randomData) {
        this(DEFAULT_BIN_COUNT, randomData);
    }

    
Private constructor to allow lazy initialisation of the RNG contained in the randomData instance variable. 
Params:
binCount – number of bins. Must be strictly positive.
randomData – Random data generator.
Throws:
NotStrictlyPositiveException – if binCount <= 0./**
     * Private constructor to allow lazy initialisation of the RNG contained
     * in the {@link #randomData} instance variable.
     *
     * @param binCount number of bins. Must be strictly positive.
     * @param randomData Random data generator.
     * @throws NotStrictlyPositiveException if {@code binCount <= 0}.
     */
    private EmpiricalDistribution(int binCount,
                                  RandomDataGenerator randomData) {
        super(randomData.getRandomGenerator());
        if (binCount <= 0) {
            throw new NotStrictlyPositiveException(binCount);
        }
        this.binCount = binCount;
        this.randomData = randomData;
        binStats = new ArrayList<SummaryStatistics>();
    }

    
Computes the empirical distribution from the provided
array of numbers.
Params:
in – the input data array
Throws:
NullArgumentException – if in is null/**
     * Computes the empirical distribution from the provided
     * array of numbers.
     *
     * @param in the input data array
     * @exception NullArgumentException if in is null
     */
    public void load(double[] in) throws NullArgumentException {
        DataAdapter da = new ArrayDataAdapter(in);
        try {
            da.computeStats();
            // new adapter for the second pass
            fillBinStats(new ArrayDataAdapter(in));
        } catch (IOException ex) {
            // Can't happen
            throw new MathInternalError();
        }
        loaded = true;

    }

    
Computes the empirical distribution using data read from a URL.
The input file must be an ASCII text file containing one
valid numeric entry per line.
Params:
url – url of the input file
Throws:
IOException – if an IO error occurs
NullArgumentException – if url is null
ZeroException – if URL contains no data/**
     * Computes the empirical distribution using data read from a URL.
     *
     * <p>The input file <i>must</i> be an ASCII text file containing one
     * valid numeric entry per line.</p>
     *
     * @param url url of the input file
     *
     * @throws IOException if an IO error occurs
     * @throws NullArgumentException if url is null
     * @throws ZeroException if URL contains no data
     */
    public void load(URL url) throws IOException, NullArgumentException, ZeroException {
        MathUtils.checkNotNull(url);
        Charset charset = Charset.forName(FILE_CHARSET);
        BufferedReader in =
            new BufferedReader(new InputStreamReader(url.openStream(), charset));
        try {
            DataAdapter da = new StreamDataAdapter(in);
            da.computeStats();
            if (sampleStats.getN() == 0) {
                throw new ZeroException(LocalizedFormats.URL_CONTAINS_NO_DATA, url);
            }
            // new adapter for the second pass
            in = new BufferedReader(new InputStreamReader(url.openStream(), charset));
            fillBinStats(new StreamDataAdapter(in));
            loaded = true;
        } finally {
           try {
               in.close();
           } catch (IOException ex) { //NOPMD
               // ignore
           }
        }
    }

    
Computes the empirical distribution from the input file.
The input file must be an ASCII text file containing one
valid numeric entry per line.
Params:
file – the input file
Throws:
IOException – if an IO error occurs
NullArgumentException – if file is null/**
     * Computes the empirical distribution from the input file.
     *
     * <p>The input file <i>must</i> be an ASCII text file containing one
     * valid numeric entry per line.</p>
     *
     * @param file the input file
     * @throws IOException if an IO error occurs
     * @throws NullArgumentException if file is null
     */
    public void load(File file) throws IOException, NullArgumentException {
        MathUtils.checkNotNull(file);
        Charset charset = Charset.forName(FILE_CHARSET);
        InputStream is = new FileInputStream(file);
        BufferedReader in = new BufferedReader(new InputStreamReader(is, charset));
        try {
            DataAdapter da = new StreamDataAdapter(in);
            da.computeStats();
            // new adapter for second pass
            is = new FileInputStream(file);
            in = new BufferedReader(new InputStreamReader(is, charset));
            fillBinStats(new StreamDataAdapter(in));
            loaded = true;
        } finally {
            try {
                in.close();
            } catch (IOException ex) { //NOPMD
                // ignore
            }
        }
    }

    
Provides methods for computing sampleStats and
beanStats abstracting the source of data.
/**
     * Provides methods for computing <code>sampleStats</code> and
     * <code>beanStats</code> abstracting the source of data.
     */
    private abstract class DataAdapter{

        
Compute bin stats.
Throws:
IOException –  if an error occurs computing bin stats/**
         * 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/**
         * 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
/**
     * <code>DataAdapter</code> for data provided through some input stream
     */
    private class StreamDataAdapter extends DataAdapter{

        
Input stream providing access to the data /** Input stream providing access to the data */
        private BufferedReader inputStream;

        
Create a StreamDataAdapter from a BufferedReader
Params:
in – BufferedReader input stream/**
         * Create a StreamDataAdapter from a BufferedReader
         *
         * @param in BufferedReader input stream
         */
        StreamDataAdapter(BufferedReader in){
            super();
            inputStream = in;
        }

        
{@inheritDoc} /** {@inheritDoc} */
        @Override
        public void computeBinStats() throws IOException {
            String str = null;
            double val = 0.0d;
            while ((str = inputStream.readLine()) != null) {
                val = Double.parseDouble(str);
                SummaryStatistics stats = binStats.get(findBin(val));
                stats.addValue(val);
            }

            inputStream.close();
            inputStream = null;
        }

        
{@inheritDoc} /** {@inheritDoc} */
        @Override
        public void computeStats() throws IOException {
            String str = null;
            double val = 0.0;
            sampleStats = new SummaryStatistics();
            while ((str = inputStream.readLine()) != null) {
                val = Double.parseDouble(str);
                sampleStats.addValue(val);
            }
            inputStream.close();
            inputStream = null;
        }
    }

    
DataAdapter for data provided as array of doubles.
/**
     * <code>DataAdapter</code> for data provided as array of doubles.
     */
    private class ArrayDataAdapter extends DataAdapter {

        
Array of input  data values /** Array of input  data values */
        private double[] inputArray;

        
Construct an ArrayDataAdapter from a double[] array
Params:
in – double[] array holding the data
Throws:
NullArgumentException – if in is null/**
         * Construct an ArrayDataAdapter from a double[] array
         *
         * @param in double[] array holding the data
         * @throws NullArgumentException if in is null
         */
        ArrayDataAdapter(double[] in) throws NullArgumentException {
            super();
            MathUtils.checkNotNull(in);
            inputArray = in;
        }

        
{@inheritDoc} /** {@inheritDoc} */
        @Override
        public void computeStats() throws IOException {
            sampleStats = new SummaryStatistics();
            for (int i = 0; i < inputArray.length; i++) {
                sampleStats.addValue(inputArray[i]);
            }
        }

        
{@inheritDoc} /** {@inheritDoc} */
        @Override
        public void computeBinStats() throws IOException {
            for (int i = 0; i < inputArray.length; i++) {
                SummaryStatistics stats =
                    binStats.get(findBin(inputArray[i]));
                stats.addValue(inputArray[i]);
            }
        }
    }

    
Fills binStats array (second pass through data file).
Params:
da – object providing access to the data
Throws:
IOException –  if an IO error occurs/**
     * Fills binStats array (second pass through data file).
     *
     * @param da object providing access to the data
     * @throws IOException  if an IO error occurs
     */
    private void fillBinStats(final DataAdapter da)
        throws IOException {
        // Set up grid
        min = sampleStats.getMin();
        max = sampleStats.getMax();
        delta = (max - min)/((double) binCount);

        // Initialize binStats ArrayList
        if (!binStats.isEmpty()) {
            binStats.clear();
        }
        for (int i = 0; i < binCount; i++) {
            SummaryStatistics stats = new SummaryStatistics();
            binStats.add(i,stats);
        }

        // Filling data in binStats Array
        da.computeBinStats();

        // Assign upperBounds based on bin counts
        upperBounds = new double[binCount];
        upperBounds[0] =
        ((double) binStats.get(0).getN()) / (double) sampleStats.getN();
        for (int i = 1; i < binCount-1; i++) {
            upperBounds[i] = upperBounds[i-1] +
            ((double) binStats.get(i).getN()) / (double) sampleStats.getN();
        }
        upperBounds[binCount-1] = 1.0d;
    }

    
Returns the index of the bin to which the given value belongs
Params:
value –  the value whose bin we are trying to find
Returns:
the index of the bin containing the value/**
     * 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
Throws:
MathIllegalStateException – if the distribution has not been loaded
Returns:
the random value./**
     * Generates a random value from this distribution.
     * <strong>Preconditions:</strong><ul>
     * <li>the distribution must be loaded before invoking this method</li></ul>
     * @return the random value.
     * @throws MathIllegalStateException if the distribution has not been loaded
     */
    public double getNextValue() throws MathIllegalStateException {

        if (!loaded) {
            throw new MathIllegalStateException(LocalizedFormats.DISTRIBUTION_NOT_LOADED);
        }

        return sample();
    }

    
Returns a StatisticalSummary describing this distribution. Preconditions:

the distribution must be loaded before invoking this method
Throws:
IllegalStateException – if the distribution has not been loaded
Returns:
the sample statistics/**
     * Returns a {@link StatisticalSummary} describing this distribution.
     * <strong>Preconditions:</strong><ul>
     * <li>the distribution must be loaded before invoking this method</li></ul>
     *
     * @return the sample statistics
     * @throws IllegalStateException if the distribution has not been loaded
     */
    public StatisticalSummary getSampleStats() {
        return sampleStats;
    }

    
Returns the number of bins.
Returns:
the number of bins./**
     * Returns the number of bins.
     *
     * @return the number of bins.
     */
    public int getBinCount() {
        return binCount;
    }

    
Returns a List of SummaryStatistics instances containing statistics describing the values in each of the bins. The list is indexed on the bin number. 
Returns:
List of bin statistics./**
     * Returns a List of {@link SummaryStatistics} instances containing
     * statistics describing the values in each of the bins.  The list is
     * indexed on the bin number.
     *
     * @return List of bin statistics.
     */
    public List<SummaryStatistics> getBinStats() {
        return binStats;
    }

    
Returns a fresh copy of the array of upper bounds for the bins.
Bins are: 

[min,upperBounds[0]],(upperBounds[0],upperBounds[1]],...,
 (upperBounds[binCount-2], upperBounds[binCount-1] = max].
Note: In versions 1.0-2.0 of commons-math, this method incorrectly returned the array of probability generator upper bounds now returned by getGeneratorUpperBounds().
Returns:
array of bin upper bounds
Since:
2.1/**
     * <p>Returns a fresh copy of the array of upper bounds for the bins.
     * Bins are: <br/>
     * [min,upperBounds[0]],(upperBounds[0],upperBounds[1]],...,
     *  (upperBounds[binCount-2], upperBounds[binCount-1] = max].</p>
     *
     * <p>Note: In versions 1.0-2.0 of commons-math, this method
     * incorrectly returned the array of probability generator upper
     * bounds now returned by {@link #getGeneratorUpperBounds()}.</p>
     *
     * @return array of bin upper bounds
     * @since 2.1
     */
    public double[] getUpperBounds() {
        double[] binUpperBounds = new double[binCount];
        for (int i = 0; i < binCount - 1; i++) {
            binUpperBounds[i] = min + delta * (i + 1);
        }
        binUpperBounds[binCount - 1] = max;
        return binUpperBounds;
    }

    
Returns a fresh copy of the array of upper bounds of the subintervals
of [0,1] used in generating data from the empirical distribution.
Subintervals correspond to bins with lengths proportional to bin counts.
Preconditions:

the distribution must be loaded before invoking this method
In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned by getUpperBounds().
Throws:
NullPointerException – unless a load method has been called beforehand.
Since:
2.1
Returns:
array of upper bounds of subintervals used in data generation/**
     * <p>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.</p>
     *
     * <strong>Preconditions:</strong><ul>
     * <li>the distribution must be loaded before invoking this method</li></ul>
     *
     * <p>In versions 1.0-2.0 of commons-math, this array was (incorrectly) returned
     * by {@link #getUpperBounds()}.</p>
     *
     * @since 2.1
     * @return array of upper bounds of subintervals used in data generation
     * @throws NullPointerException unless a {@code load} method has been
     * called beforehand.
     */
    public double[] getGeneratorUpperBounds() {
        int len = upperBounds.length;
        double[] out = new double[len];
        System.arraycopy(upperBounds, 0, out, 0, len);
        return out;
    }

    
Property indicating whether or not the distribution has been loaded.
Returns:
true if the distribution has been loaded/**
     * 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 getNextValue(). 
Params:
seed – random generator seed
Since:
3.0/**
     * Reseeds the random number generator used by {@link #getNextValue()}.
     *
     * @param seed random generator seed
     * @since 3.0
     */
    public void reSeed(long seed) {
        randomData.reSeed(seed);
    }

    // Distribution methods ---------------------------

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    @Override
    public double probability(double x) {
        return 0;
    }

    
{@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.

Since:
3.1/**
     * {@inheritDoc}
     *
     * <p>Returns the kernel density normalized so that its integral over each bin
     * equals the bin mass.</p>
     *
     * <p>Algorithm description: <ol>
     * <li>Find the bin B that x belongs to.</li>
     * <li>Compute K(B) = the mass of B with respect to the within-bin kernel (i.e., the
     * integral of the kernel density over B).</li>
     * <li>Return k(x) * P(B) / K(B), where k is the within-bin kernel density
     * and P(B) is the mass of B.</li></ol></p>
     * @since 3.1
     */
    public double density(double x) {
        if (x < min || x > max) {
            return 0d;
        }
        final int binIndex = findBin(x);
        final RealDistribution kernel = getKernel(binStats.get(binIndex));
        return kernel.density(x) * pB(binIndex) / kB(binIndex);
    }

    
{@inheritDoc}
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).

Since:
3.1/**
     * {@inheritDoc}
     *
     * <p>Algorithm description:<ol>
     * <li>Find the bin B that x belongs to.</li>
     * <li>Compute P(B) = the mass of B and P(B-) = the combined mass of the bins below B.</li>
     * <li>Compute K(B) = the probability mass of B with respect to the within-bin kernel
     * and K(B-) = the kernel distribution evaluated at the lower endpoint of B</li>
     * <li>Return P(B-) + P(B) * [K(x) - K(B-)] / K(B) where
     * K(x) is the within-bin kernel distribution function evaluated at x.</li></ol>
     * If K is a constant distribution, we return P(B-) + P(B) (counting the full
     * mass of B).</p>
     *
     * @since 3.1
     */
    public double cumulativeProbability(double x) {
        if (x < min) {
            return 0d;
        } else if (x >= max) {
            return 1d;
        }
        final int binIndex = findBin(x);
        final double pBminus = pBminus(binIndex);
        final double pB = pB(binIndex);
        final RealDistribution kernel = k(x);
        if (kernel instanceof ConstantRealDistribution) {
            if (x < kernel.getNumericalMean()) {
                return pBminus;
            } else {
                return pBminus + pB;
            }
        }
        final double[] binBounds = getUpperBounds();
        final double kB = kB(binIndex);
        final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
        final double withinBinCum =
            (kernel.cumulativeProbability(x) -  kernel.cumulativeProbability(lower)) / kB;
        return pBminus + pB * withinBinCum;
    }

    
{@inheritDoc}
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) 
 

Since:
3.1/**
     * {@inheritDoc}
     *
     * <p>Algorithm description:<ol>
     * <li>Find the smallest i such that the sum of the masses of the bins
     *  through i is at least p.</li>
     * <li>
     *   Let K be the within-bin kernel distribution for bin i.</br>
     *   Let K(B) be the mass of B under K. <br/>
     *   Let K(B-) be K evaluated at the lower endpoint of B (the combined
     *   mass of the bins below B under K).<br/>
     *   Let P(B) be the probability of bin i.<br/>
     *   Let P(B-) be the sum of the bin masses below bin i. <br/>
     *   Let pCrit = p - P(B-)<br/>
     * <li>Return the inverse of K evaluated at <br/>
     *    K(B-) + pCrit * K(B) / P(B) </li>
     *  </ol></p>
     *
     * @since 3.1
     */
    @Override
    public double inverseCumulativeProbability(final double p) throws OutOfRangeException {
        if (p < 0.0 || p > 1.0) {
            throw new OutOfRangeException(p, 0, 1);
        }

        if (p == 0.0) {
            return getSupportLowerBound();
        }

        if (p == 1.0) {
            return getSupportUpperBound();
        }

        int i = 0;
        while (cumBinP(i) < p) {
            i++;
        }

        final RealDistribution kernel = getKernel(binStats.get(i));
        final double kB = kB(i);
        final double[] binBounds = getUpperBounds();
        final double lower = i == 0 ? min : binBounds[i - 1];
        final double kBminus = kernel.cumulativeProbability(lower);
        final double pB = pB(i);
        final double pBminus = pBminus(i);
        final double pCrit = p - pBminus;
        if (pCrit <= 0) {
            return lower;
        }
        return kernel.inverseCumulativeProbability(kBminus + pCrit * kB / pB);
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public double getNumericalMean() {
       return sampleStats.getMean();
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public double getNumericalVariance() {
        return sampleStats.getVariance();
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public double getSupportLowerBound() {
       return min;
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public double getSupportUpperBound() {
        return max;
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public boolean isSupportLowerBoundInclusive() {
        return true;
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public boolean isSupportUpperBoundInclusive() {
        return true;
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    public boolean isSupportConnected() {
        return true;
    }

    
{@inheritDoc}
Since:
3.1/**
     * {@inheritDoc}
     * @since 3.1
     */
    @Override
    public void reseedRandomGenerator(long seed) {
        randomData.reSeed(seed);
    }

    
The probability of bin i.
Params:
i – the index of the bin
Returns:
the probability that selection begins in bin i/**
     * 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.
Params:
i – the index of the bin
Returns:
the probability that selection begins in a bin below bin i./**
     * 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.
Params:
i – index of the bin
Returns:
the difference in the within-bin kernel cdf between the
upper and lower endpoints of bin i/**
     * Mass of bin i under the within-bin kernel of the bin.
     *
     * @param i index of the bin
     * @return the difference in the within-bin kernel cdf between the
     * upper and lower endpoints of bin i
     */
    @SuppressWarnings("deprecation")
    private double kB(int i) {
        final double[] binBounds = getUpperBounds();
        final RealDistribution kernel = getKernel(binStats.get(i));
        return i == 0 ? kernel.cumulativeProbability(min, binBounds[0]) :
            kernel.cumulativeProbability(binBounds[i - 1], binBounds[i]);
    }

    
The within-bin kernel of the bin that x belongs to.
Params:
x – the value to locate within a bin
Returns:
the within-bin kernel of the bin containing x/**
     * 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.
Params:
binIndex – maximum bin index
Returns:
sum of the probabilities of bins through 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 bStats, unless the bin contains only one observation, in which case a constant distribution is returned. 
Params:
bStats – summary statistics for the bin
Returns:
within-bin kernel parameterized by bStats/**
     * The within-bin smoothing kernel. Returns a Gaussian distribution
     * parameterized by {@code bStats}, unless the bin contains only one
     * observation, in which case a constant distribution is returned.
     *
     * @param bStats summary statistics for the bin
     * @return within-bin kernel parameterized by bStats
     */
    protected RealDistribution getKernel(SummaryStatistics bStats) {
        if (bStats.getN() == 1 || bStats.getVariance() == 0) {
            return new ConstantRealDistribution(bStats.getMean());
        } else {
            return new NormalDistribution(randomData.getRandomGenerator(),
                bStats.getMean(), bStats.getStandardDeviation(),
                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
        }
    }
}