Examples of cumulativeProbability()

@param x the value at which the CDF is evaluated. @return CDF for this distribution. @throws MathException if the cumulative probability can not becomputed due to convergence or other numerical errors.
  • org.apache.commons.math.distribution.NormalDistributionImpl.cumulativeProbability()
    For this distribution, X, this method returns P(X < x). If xis more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is within Double.MIN_VALUE of 0 or 1. @param x the value at which the CDF is evaluated. @return CDF evaluated at x. @throws MathException if the algorithm fails to converge
  • org.apache.commons.math.distribution.PoissonDistribution.cumulativeProbability()
  • org.apache.commons.math.distribution.PoissonDistributionImpl.cumulativeProbability()
    The probability distribution function P(X <= x) for a Poisson distribution. @param x the value at which the PDF is evaluated. @return Poisson distribution function evaluated at x @throws MathException if the cumulative probability can not be computeddue to convergence or other numerical errors.
  • org.apache.commons.math.distribution.TDistribution.cumulativeProbability()
  • org.apache.commons.math.distribution.TDistributionImpl.cumulativeProbability()
    For this distribution, X, this method returns P(X < x). @param x the value at which the CDF is evaluated. @return CDF evaluated at x. @throws MathException if the cumulative probability can not becomputed due to convergence or other numerical errors.
  • org.apache.commons.math.distribution.WeibullDistribution.cumulativeProbability()
  • org.apache.commons.math3.distribution.BetaDistribution.cumulativeProbability()
    {@inheritDoc}
  • org.apache.commons.math3.distribution.BinomialDistribution.cumulativeProbability()
    {@inheritDoc}
  • org.apache.commons.math3.distribution.ChiSquaredDistribution.cumulativeProbability()
    {@inheritDoc}
  • org.apache.commons.math3.distribution.FDistribution.cumulativeProbability()
    orld.wolfram.com/F-Distribution.html"> F-Distribution, equation (4).
  • org.apache.commons.math3.distribution.GammaDistribution.cumulativeProbability()
    orld.wolfram.com/Chi-SquaredDistribution.html"> Chi-Squared Distribution, equation (9).
  • Casella, G., & Berger, R. (1990). Statistical Inference. Belmont, CA: Duxbury Press.
  • org.apache.commons.math3.distribution.IntegerDistribution.cumulativeProbability()
    For a random variable {@code X} whose values are distributed accordingto this distribution, this method returns {@code P(X <= x)}. In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. @param x the point at which the CDF is evaluated @return the probability that a random variable with thisdistribution takes a value less than or equal to {@code x}
  • org.apache.commons.math3.distribution.NormalDistribution.cumulativeProbability()
    {@inheritDoc}If {@code x} is more than 40 standard deviations from the mean, 0 or 1is returned, as in these cases the actual value is within {@code Double.MIN_VALUE} of 0 or 1.
  • org.apache.commons.math3.distribution.PoissonDistribution.cumulativeProbability()
    {@inheritDoc}
  • org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()
    For a random variable {@code X} whose values are distributed accordingto this distribution, this method returns {@code P(x0 < X <= x1)}. @param x0 the exclusive lower bound @param x1 the inclusive upper bound @return the probability that a random variable with this distributiontakes a value between {@code x0} and {@code x1}, excluding the lower and including the upper endpoint @throws NumberIsTooLargeException if {@code x0> x1} @deprecated As of 3.1. In 4.0, this method will be renamed{@code probability(double x0, double x1)}.
  • org.apache.commons.math3.distribution.TDistribution.cumulativeProbability()
    {@inheritDoc}

    • Examples of org.apache.commons.math3.distribution.PoissonDistribution.cumulativeProbability()

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            // Top bin
            observed[binCount - 1] = 0;
            for (int i = upper; i <= maxObservedValue; i++) {
                observed[binCount - 1] += frequency.getCount(i);
            }
            expected[binCount - 1] = (1 - poissonDistribution.cumulativeProbability(upper - 1)) * sampleSize;

            // Interior bins
            for (int i = 1; i < binCount - 1; i++) {
                observed[i] = 0;
                for (int j = binBounds.get(i - 1); j < binBounds.get(i); j++) {
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    Examples of org.apache.commons.math3.distribution.PoissonDistribution.cumulativeProbability()

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            for (int i = 1; i < binCount - 1; i++) {
                observed[i] = 0;
                for (int j = binBounds.get(i - 1); j < binBounds.get(i); j++) {
                    observed[i] += frequency.getCount(j);
                } // Expected count is (mass in [binBounds[i-1], binBounds[i])) * sampleSize
                expected[i] = (poissonDistribution.cumulativeProbability(binBounds.get(i) - 1) -
                    poissonDistribution.cumulativeProbability(binBounds.get(i - 1) -1)) * sampleSize;
            }

            // Use chisquare test to verify that generated values are poisson(mean)-distributed
            ChiSquareTest chiSquareTest = new ChiSquareTest();
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    Examples of org.apache.commons.math3.distribution.PoissonDistribution.cumulativeProbability()

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                observed[i] = 0;
                for (int j = binBounds.get(i - 1); j < binBounds.get(i); j++) {
                    observed[i] += frequency.getCount(j);
                } // Expected count is (mass in [binBounds[i-1], binBounds[i])) * sampleSize
                expected[i] = (poissonDistribution.cumulativeProbability(binBounds.get(i) - 1) -
                    poissonDistribution.cumulativeProbability(binBounds.get(i - 1) -1)) * sampleSize;
            }

            // Use chisquare test to verify that generated values are poisson(mean)-distributed
            ChiSquareTest chiSquareTest = new ChiSquareTest();
                // Fail if we can reject null hypothesis that distributions are the same
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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            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}
     
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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            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}
     
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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            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;
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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         */
        @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.
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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        @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.
         *
     
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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                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;
        }
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    Examples of org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability()

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                // 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;
        }

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