Package org.apache.commons.math3.distribution

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

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            if (Math.abs(approx - actual) <= error) {
                inRange++;
            }
        }

        BinomialDistribution binomial = new BinomialDistribution(numberOfRuns, getConfidence());
        int lowerBound = binomial.inverseCumulativeProbability(0.01);
        int upperBound = binomial.inverseCumulativeProbability(0.99);
        assertTrue(lowerBound < inRange && inRange < upperBound, String.format("%d out of %d passed. Expected [%d, %d]", inRange, numberOfRuns, lowerBound, upperBound));
    }
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        BinomialDistributionTest testInstance = new BinomialDistributionTest();
        int[] densityPoints = testInstance.makeDensityTestPoints();
        double[] densityValues = testInstance.makeDensityTestValues();
        int sampleSize = 1000;
        int length = TestUtils.eliminateZeroMassPoints(densityPoints, densityValues);
        BinomialDistribution distribution = (BinomialDistribution) 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.nextBinomial(distribution.getNumberOfTrials(),
                  distribution.getProbabilityOfSuccess());
          for (int j = 0; j < length; j++) {
              if (value == densityPoints[j]) {
                  observedCounts[j]++;
              }
          }
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     * @param numberOfTrials number of trials of the Binomial distribution
     * @param probabilityOfSuccess probability of success of the Binomial distribution
     * @return random value sampled from the Binomial(numberOfTrials, probabilityOfSuccess) distribution
     */
    public int nextBinomial(int numberOfTrials, double probabilityOfSuccess) {
        return new BinomialDistribution(getRandomGenerator(), numberOfTrials, probabilityOfSuccess).sample();
    }
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        double p = 0.5;

        if (N > 30) {
            NormalDistribution n = new NormalDistribution(N * p, Math.sqrt(N * p * (1 - p)));
        } else {
            BinomialDistribution bn = new BinomialDistribution((int) N, p);
            double observed = di.getDeletionDepth();
        }

        return pval;
    }
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            }
        }
    }

    public void test() {
        BinomialDistribution bn = new BinomialDistribution(120, 0.5);
        NormalDistribution n = new NormalDistribution(60, Math.sqrt(30));

        PVector param_norm = new PVector(2);
        param_norm.array[0] = 60;   // mean
        param_norm.array[1] = 30;   // var

        PVector param_bino = new PVector(2);
        param_bino.array[0] = 120;   // n
        param_bino.array[1] = 0.5;   // p

        ExponentialFamily normal = new UnivariateGaussian();
        PVector p = new PVector(1);
        p.array[0] = 32;

        System.out.println(bn.cumulativeProbability(32));
        System.out.println(n.cumulativeProbability(32));
        System.out.println(normal.density(p, param_norm));

        p.array[0] = 27;
        System.out.println(bn.cumulativeProbability(27));
        System.out.println(n.cumulativeProbability(27));
        System.out.println(n.density(27));
        System.out.println(normal.density(p, param_norm));

        p.array[0] = 60;
        System.out.println(bn.cumulativeProbability(60));
        System.out.println(n.cumulativeProbability(60));
        System.out.println(n.density(60));
        System.out.println(normal.density(p, param_norm));

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     * @param numberOfTrials number of trials of the Binomial distribution
     * @param probabilityOfSuccess probability of success of the Binomial distribution
     * @return random value sampled from the Binomial(numberOfTrials, probabilityOfSuccess) distribution
     */
    public int nextBinomial(int numberOfTrials, double probabilityOfSuccess) {
        return new BinomialDistribution(getRan(), numberOfTrials, probabilityOfSuccess).sample();
    }
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        BinomialDistributionTest testInstance = new BinomialDistributionTest();
        int[] densityPoints = testInstance.makeDensityTestPoints();
        double[] densityValues = testInstance.makeDensityTestValues();
        int sampleSize = 1000;
        int length = TestUtils.eliminateZeroMassPoints(densityPoints, densityValues);
        BinomialDistribution distribution = (BinomialDistribution) 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.nextBinomial(distribution.getNumberOfTrials(),
                  distribution.getProbabilityOfSuccess());
          for (int j = 0; j < length; j++) {
              if (value == densityPoints[j]) {
                  observedCounts[j]++;
              }
          }
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            if (Math.abs(approx - actual) <= error) {
                inRange++;
            }
        }

        BinomialDistribution binomial = new BinomialDistribution(numberOfRuns, getConfidence());
        int lowerBound = binomial.inverseCumulativeProbability(0.01);
        int upperBound = binomial.inverseCumulativeProbability(0.99);
        assertTrue(lowerBound < inRange && inRange < upperBound, String.format("%d out of %d passed. Expected [%d, %d]", inRange, numberOfRuns, lowerBound, upperBound));
    }
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            }
            if (alternativeHypothesis == null) {
                throw new NullArgumentException();
            }

            final BinomialDistribution distribution = new BinomialDistribution(numberOfTrials, probability);
            switch (alternativeHypothesis) {
                case GREATER_THAN:
                    return 1 - distribution.cumulativeProbability(numberOfSuccesses - 1);
                case LESS_THAN:
                    return distribution.cumulativeProbability(numberOfSuccesses);
                case TWO_SIDED:
                    int criticalValueLow = 0;
                    int criticalValueHigh = numberOfTrials;
                    double pTotal = 0;

                    while (true) {
                        double pLow = distribution.probability(criticalValueLow);
                        double pHigh = distribution.probability(criticalValueHigh);

                        if (pLow == pHigh) {
                            pTotal += 2 * pLow;
                            criticalValueLow++;
                            criticalValueHigh--;
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    @Test
    public void testErrorBound()
            throws Exception
    {
        int trials = 20;
        BinomialDistribution binomial = new BinomialDistribution(trials, 0.5);

        int successes = 0;
        Random rand = new Random(0);
        for (int i = 0; i < trials; i++) {
            int sum = 1_000;
            PageBuilder builder = new PageBuilder(ImmutableList.of(BIGINT, BIGINT));
            for (int j = 0; j < sum; j++) {
                if (rand.nextDouble() < 0.5) {
                    builder.getBlockBuilder(0).appendLong(1);
                    builder.getBlockBuilder(1).appendLong(2);
                }
            }

            AggregationFunction function = new DeterministicBootstrappedAggregation(createTestingBlockEncodingManager(), LONG_SUM);

            successes += approximateAggregationWithinErrorBound(function, 1, 0.5, (double) sum, builder.build()) ? 1 : 0;
        }

        // Since we used a confidence of 0.5, successes should have a binomial distribution B(n=20, p=0.5)
        assertTrue(binomial.inverseCumulativeProbability(0.01) < successes && successes < binomial.inverseCumulativeProbability(0.99));
    }
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  • org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
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  • org.apache.commons.math3.analysis.function.Sinc
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  • org.apache.commons.math3.analysis.QuinticFunction
  • org.apache.commons.math3.analysis.solvers.BrentSolver
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