Java Code Examples for org.apache.commons.math3.distribution.RealDistribution#cumulativeProbability()

/**
 * Computes the one-sample Kolmogorov-Smirnov test statistic, \(D_n=\sup_x |F_n(x)-F(x)|\) where
 * \(F\) is the distribution (cdf) function associated with {@code distribution}, \(n\) is the
 * length of {@code data} and \(F_n\) is the empirical distribution that puts mass \(1/n\) at
 * each of the values in {@code data}.
 *
 * @param distribution reference distribution
 * @param data sample being evaluated
 * @return Kolmogorov-Smirnov statistic \(D_n\)
 * @throws InsufficientDataException if {@code data} does not have length at least 2
 * @throws NullArgumentException if {@code data} is null
 */
public double kolmogorovSmirnovStatistic(RealDistribution distribution, double[] data) {
    checkArray(data);
    final int n = data.length;
    final double nd = n;
    final double[] dataCopy = new double[n];
    System.arraycopy(data, 0, dataCopy, 0, n);
    Arrays.sort(dataCopy);
    double d = 0d;
    for (int i = 1; i <= n; i++) {
        final double yi = distribution.cumulativeProbability(dataCopy[i - 1]);
        final double currD = FastMath.max(yi - (i - 1) / nd, i / nd - yi);
        if (currD > d) {
            d = currD;
        }
    }
    return d;
}
 

/**
 * {@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></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 double[] binBounds = getUpperBounds();
    final double kB = kB(binIndex);
    final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
    final RealDistribution kernel = k(x);
    final double withinBinCum =
        (kernel.cumulativeProbability(x) -  kernel.cumulativeProbability(lower)) / kB;
    return pBminus + pB * withinBinCum;
}
 

/**
 * Computes the one-sample Kolmogorov-Smirnov test statistic, \(D_n=\sup_x |F_n(x)-F(x)|\) where
 * \(F\) is the distribution (cdf) function associated with {@code distribution}, \(n\) is the
 * length of {@code data} and \(F_n\) is the empirical distribution that puts mass \(1/n\) at
 * each of the values in {@code data}.
 *
 * @param distribution reference distribution
 * @param data sample being evaluated
 * @return Kolmogorov-Smirnov statistic \(D_n\)
 * @throws InsufficientDataException if {@code data} does not have length at least 2
 * @throws NullArgumentException if {@code data} is null
 */
public double kolmogorovSmirnovStatistic(RealDistribution distribution, double[] data) {
    checkArray(data);
    final int n = data.length;
    final double nd = n;
    final double[] dataCopy = new double[n];
    System.arraycopy(data, 0, dataCopy, 0, n);
    Arrays.sort(dataCopy);
    double d = 0d;
    for (int i = 1; i <= n; i++) {
        final double yi = distribution.cumulativeProbability(dataCopy[i - 1]);
        final double currD = FastMath.max(yi - (i - 1) / nd, i / nd - yi);
        if (currD > d) {
            d = currD;
        }
    }
    return d;
}
 

@Override
public double[] makeDensityTestValues() {
    final double[] testPoints = getCumulativeTestPoints();
    final double[] densityValues = new double[testPoints.length];
    final EmpiricalDistribution empiricalDistribution = (EmpiricalDistribution) makeDistribution();
    final double[] binBounds = empiricalDistribution.getUpperBounds();
    for (int i = 0; i < testPoints.length; i++) {
        final int bin = findBin(testPoints[i]);
        final double lower = bin == 0 ? empiricalDistribution.getSupportLowerBound() :
            binBounds[bin - 1];
        final double upper = binBounds[bin];
        final RealDistribution kernel = findKernel(lower, upper);
        final double withinBinKernelMass = kernel.cumulativeProbability(lower, upper);
        final double density = kernel.density(testPoints[i]);
        densityValues[i] = density * (bin == 0 ? firstBinMass : binMass) / withinBinKernelMass;   
    }
    return densityValues;
}
 

public static void addCDFSeries(Chart chart, RealDistribution distribution, String desc, int lowerBound, int upperBound) {
    // generates Log data
    List<Number> xData = new ArrayList<Number>();
    List<Number> yData = new ArrayList<Number>();
    int samples = 100;
    double stepSize = (upperBound - lowerBound) / (double) samples;
    for (double x = lowerBound; x <= upperBound; x += stepSize) {
      double density = distribution.cumulativeProbability(x);
      if (! Double.isInfinite(density) && ! Double.isNaN(density)) {
          xData.add(x);
          yData.add(density);
      }
    }

    Series series = chart.addSeries(desc, xData, yData);
    series.setMarker(SeriesMarker.NONE);
    series.setLineStyle(new BasicStroke(1.2f));
}
 

@Override
public double[] makeCumulativeTestValues() {
    /* 
     * Bins should be [0, 10], (10, 20], ..., (9990, 10000]
     * Kernels should be N(4.5, 3.02765), N(14.5, 3.02765)...
     * Each bin should have mass 10/10000 = .001
     */
    final double[] testPoints = getCumulativeTestPoints();
    final double[] cumValues = new double[testPoints.length];
    final EmpiricalDistribution empiricalDistribution = (EmpiricalDistribution) makeDistribution();
    final double[] binBounds = empiricalDistribution.getUpperBounds();
    for (int i = 0; i < testPoints.length; i++) {
        final int bin = findBin(testPoints[i]);
        final double lower = bin == 0 ? empiricalDistribution.getSupportLowerBound() :
            binBounds[bin - 1];
        final double upper = binBounds[bin];
        // Compute bMinus = sum or mass of bins below the bin containing the point
        // First bin has mass 11 / 10000, the rest have mass 10 / 10000.
        final double bMinus = bin == 0 ? 0 : (bin - 1) * binMass + firstBinMass;
        final RealDistribution kernel = findKernel(lower, upper);
        final double withinBinKernelMass = kernel.cumulativeProbability(lower, upper);
        final double kernelCum = kernel.cumulativeProbability(lower, testPoints[i]);
        cumValues[i] = bMinus + (bin == 0 ? firstBinMass : binMass) * kernelCum/withinBinKernelMass;
    }
    return cumValues;
}
 

/**
 * {@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></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 double[] binBounds = getUpperBounds();
    final double kB = kB(binIndex);
    final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
    final RealDistribution kernel = k(x);
    final double withinBinCum =
        (kernel.cumulativeProbability(x) -  kernel.cumulativeProbability(lower)) / kB;
    return pBminus + pB * withinBinCum;
}
 

/**
 * {@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></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 double[] binBounds = getUpperBounds();
    final double kB = kB(binIndex);
    final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
    final RealDistribution kernel = k(x);
    final double withinBinCum =
        (kernel.cumulativeProbability(x) -  kernel.cumulativeProbability(lower)) / kB;
    return pBminus + pB * withinBinCum;
}
 

public static void addCDFSeries(Chart chart, RealDistribution distribution, String desc, int lowerBound, int upperBound) {
    // generates Log data
    List<Number> xData = new ArrayList<Number>();
    List<Number> yData = new ArrayList<Number>();
    int samples = 100;
    double stepSize = (upperBound - lowerBound) / (double) samples;
    for (double x = lowerBound; x <= upperBound; x += stepSize) {
      double density = distribution.cumulativeProbability(x);
      if (! Double.isInfinite(density) && ! Double.isNaN(density)) {
          xData.add(x);
          yData.add(density);
      }
    }

    Series series = chart.addSeries(desc, xData, yData);
    series.setMarker(SeriesMarker.NONE);
    series.setLineStyle(new BasicStroke(1.2f));
}
 

@Override
public double[] makeCumulativeTestValues() {
    /* 
     * Bins should be [0, 10], (10, 20], ..., (9990, 10000]
     * Kernels should be N(4.5, 3.02765), N(14.5, 3.02765)...
     * Each bin should have mass 10/10000 = .001
     */
    final double[] testPoints = getCumulativeTestPoints();
    final double[] cumValues = new double[testPoints.length];
    final EmpiricalDistribution empiricalDistribution = (EmpiricalDistribution) makeDistribution();
    final double[] binBounds = empiricalDistribution.getUpperBounds();
    for (int i = 0; i < testPoints.length; i++) {
        final int bin = findBin(testPoints[i]);
        final double lower = bin == 0 ? empiricalDistribution.getSupportLowerBound() :
            binBounds[bin - 1];
        final double upper = binBounds[bin];
        // Compute bMinus = sum or mass of bins below the bin containing the point
        // First bin has mass 11 / 10000, the rest have mass 10 / 10000.
        final double bMinus = bin == 0 ? 0 : (bin - 1) * binMass + firstBinMass;
        final RealDistribution kernel = findKernel(lower, upper);
        final double withinBinKernelMass = kernel.cumulativeProbability(lower, upper);
        final double kernelCum = kernel.cumulativeProbability(lower, testPoints[i]);
        cumValues[i] = bMinus + (bin == 0 ? firstBinMass : binMass) * kernelCum/withinBinKernelMass;
    }
    return cumValues;
}
 

@Override
public double[] makeDensityTestValues() {
    final double[] testPoints = getCumulativeTestPoints();
    final double[] densityValues = new double[testPoints.length];
    final EmpiricalDistribution empiricalDistribution = (EmpiricalDistribution) makeDistribution();
    final double[] binBounds = empiricalDistribution.getUpperBounds();
    for (int i = 0; i < testPoints.length; i++) {
        final int bin = findBin(testPoints[i]);
        final double lower = bin == 0 ? empiricalDistribution.getSupportLowerBound() :
            binBounds[bin - 1];
        final double upper = binBounds[bin];
        final RealDistribution kernel = findKernel(lower, upper);
        final double withinBinKernelMass = kernel.cumulativeProbability(lower, upper);
        final double density = kernel.density(testPoints[i]);
        densityValues[i] = density * (bin == 0 ? firstBinMass : binMass) / withinBinKernelMass;   
    }
    return densityValues;
}
 

/**
 * {@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></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 double[] binBounds = getUpperBounds();
    final double kB = kB(binIndex);
    final double lower = binIndex == 0 ? min : binBounds[binIndex - 1];
    final RealDistribution kernel = k(x);
    final double withinBinCum =
        (kernel.cumulativeProbability(x) -  kernel.cumulativeProbability(lower)) / kB;
    return pBminus + pB * withinBinCum;
}
 

/**
 * {@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);
}
 

/**
 * 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]);
}
 

/**
 * {@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);
}
 

/**
 * 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]);
}
 

/**
 * 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]);
}
 

/**
 * 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]);
}
 

/**
 * {@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);
}
 

/**
 * Cumulative distribution function at x
 * @param dis Distribution.
 * @param x X.
 * @return Cumulative distribution value.
 */
public static double cdf(RealDistribution dis, Number x){
    return dis.cumulativeProbability(x.doubleValue());
}