Examples of org.apache.commons.math3.distribution.PascalDistribution

Package org.apache.commons.math3.distribution

Examples of org.apache.commons.math3.distribution.PascalDistribution

org.apache.commons.math3.exception.ConvergenceException
orld.wolfram.com/NegativeBinomialDistribution.html">MathWorld, but not in Wikipedia.

For a random variable {@code X} whose values are distributed according to thisdistribution, the probability mass function is given by
{@code P(X = k) = C(k + r - 1, r - 1) * p^r * (1 - p)^k,}
where {@code r} is the number of successes, {@code p} is the probability ofsuccess, and {@code X} is the total number of failures. {@code C(n, k)} isthe binomial coefficient ( {@code n} choose {@code k}). The mean and variance of {@code X} are
{@code E(X) = (1 - p) * r / p, var(X) = (1 - p) * r / p^2.}
Finally, the cumulative distribution function is given by
{@code P(X <= k) = I(p, r, k + 1)}, where I is the regularized incomplete Beta function.
@see Negative binomial distribution (Wikipedia) @see Negative binomial distribution (MathWorld) @since 1.2 (changed to concrete class in 3.0)


  public SamplingLongPrimitiveIterator(RandomWrapper random, LongPrimitiveIterator delegate, double samplingRate) {
    Preconditions.checkNotNull(delegate);
    Preconditions.checkArgument(samplingRate > 0.0 && samplingRate <= 1.0);
    // Geometric distribution is special case of negative binomial (aka Pascal) with r=1:
    geometricDistribution = new PascalDistribution(random.getRandomGenerator(), 1, samplingRate);
    this.delegate = delegate;
    this.hasNext = true;
    doNext();
  }

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  public SamplingLongPrimitiveIterator(RandomGenerator random, LongPrimitiveIterator delegate, double samplingRate) {
    Preconditions.checkNotNull(random);
    Preconditions.checkNotNull(delegate);
    Preconditions.checkArgument(samplingRate > 0.0 && samplingRate <= 1.0);
    // Geometric distribution is special case of negative binomial (aka Pascal) with r=1:
    geometricDistribution = new PascalDistribution(random, 1, samplingRate);
    this.delegate = delegate;
    this.hasNext = true;
    doNext();
  }

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      // No sampling at all, we can't fill the map with one pass even
      pascalDistribution = null;
    } else {
      // Number of un-selected elements to skip between selections is geometrically distributed with
      // parameter p; this is the same as a negative binomial / Pascal distribution with r=1:
      pascalDistribution = new PascalDistribution(RandomManager.getRandom(), 1, p);
    }


    LongPrimitiveIterator keyIterator = vectors.keySetIterator();
    Node[][] map = new Node[mapSize][mapSize];
    for (Node[] mapRow : map) {

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     * @throws NotStrictlyPositiveException if the number of successes is not positive
     * @throws OutOfRangeException if the probability of success is not in the
     * range {@code [0, 1]}.
     */
    public int nextPascal(int r, double p) throws NotStrictlyPositiveException, OutOfRangeException {
        return new PascalDistribution(getRan(), r, p).sample();
    }

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        PascalDistributionTest testInstance = new PascalDistributionTest();
        int[] densityPoints = testInstance.makeDensityTestPoints();
        double[] densityValues = testInstance.makeDensityTestValues();
        int sampleSize = 1000;
        int length = TestUtils.eliminateZeroMassPoints(densityPoints, densityValues);
        PascalDistribution distribution = (PascalDistribution) testInstance.makeDistribution();
        double[] expectedCounts = new double[length];
        long[] observedCounts = new long[length];
        for (int i = 0; i < length; i++) {
            expectedCounts[i] = sampleSize * densityValues[i];
        }
        randomData.reSeed(1000);
        for (int i = 0; i < sampleSize; i++) {
          int value = randomData.nextPascal(distribution.getNumberOfSuccesses(), distribution.getProbabilityOfSuccess());
          for (int j = 0; j < length; j++) {
              if (value == densityPoints[j]) {
                  observedCounts[j]++;
              }
          }

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  public SamplingIterator(RandomWrapper random, Iterator<? extends T> delegate, double samplingRate) {
    Preconditions.checkNotNull(delegate);
    Preconditions.checkArgument(samplingRate > 0.0 && samplingRate <= 1.0,
        "Must be: 0.0 < samplingRate <= 1.0. But samplingRate = " + samplingRate);
    // Geometric distribution is special case of negative binomial (aka Pascal) with r=1:
    geometricDistribution = new PascalDistribution(random.getRandomGenerator(), 1, samplingRate);
    this.delegate = delegate;
  }

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  public SamplingLongPrimitiveIterator(RandomWrapper random, LongPrimitiveIterator delegate, double samplingRate) {
    Preconditions.checkNotNull(delegate);
    Preconditions.checkArgument(samplingRate > 0.0 && samplingRate <= 1.0, "Must be: 0.0 < samplingRate <= 1.0");
    // Geometric distribution is special case of negative binomial (aka Pascal) with r=1:
    geometricDistribution = new PascalDistribution(random.getRandomGenerator(), 1, samplingRate);
    this.delegate = delegate;
    this.hasNext = true;
    doNext();
  }

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        PascalDistributionTest testInstance = new PascalDistributionTest();
        int[] densityPoints = testInstance.makeDensityTestPoints();
        double[] densityValues = testInstance.makeDensityTestValues();
        int sampleSize = 1000;
        int length = TestUtils.eliminateZeroMassPoints(densityPoints, densityValues);
        PascalDistribution distribution = (PascalDistribution) testInstance.makeDistribution();
        double[] expectedCounts = new double[length];
        long[] observedCounts = new long[length];
        for (int i = 0; i < length; i++) {
            expectedCounts[i] = sampleSize * densityValues[i];
        }
        randomData.reSeed(1000);
        for (int i = 0; i < sampleSize; i++) {
          int value = randomData.nextPascal(distribution.getNumberOfSuccesses(), distribution.getProbabilityOfSuccess());
          for (int j = 0; j < length; j++) {
              if (value == densityPoints[j]) {
                  observedCounts[j]++;
              }
          }

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                // tests for termination and stringent tolerances
                if (FastMath.abs(actRed) <= TWO_EPS &&
                    preRed <= TWO_EPS &&
                    ratio <= 2.0) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_COST_RELATIVE_TOLERANCE,
                                                   costRelativeTolerance);
                } else if (delta <= TWO_EPS * xNorm) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_PARAMETERS_RELATIVE_TOLERANCE,
                                                   parRelativeTolerance);
                } else if (maxCosine <= TWO_EPS) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_ORTHOGONALITY_TOLERANCE,
                                                   orthoTolerance);
                }
            }
        }
    }

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                for (int j = k; j < nR; ++j) {
                    double aki = weightedJacobian[j][permutation[i]];
                    norm2 += aki * aki;
                }
                if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
                    throw new ConvergenceException(LocalizedFormats.UNABLE_TO_PERFORM_QR_DECOMPOSITION_ON_JACOBIAN,
                                                   nR, nC);
                }
                if (norm2 > ak2) {
                    nextColumn = i;
                    ak2        = norm2;

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