Examples of org.apache.commons.math3.distribution.FDistribution.cumulativeProbability()

            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;
    }

        };
        final double[] lower = {0, 5, 1000, 5001, 9995};
        final double[] upper = {5, 12, 1030, 5010, 10000};
        for (int i = 1; i < 5; i++) {
            Assert.assertEquals(
                    distribution.cumulativeProbability( 
                            lower[i], upper[i]),
                            integrator.integrate(
                                    1000000, // Triangle integrals are very slow to converge
                                    d, lower[i], upper[i]), tol);
        }

        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}

        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}


        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;

     */
    @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.

    @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.
     *

        if (n < 3) {
            return Double.NaN;
        }
        // No advertised NotStrictlyPositiveException here - will return NaN above
        TDistribution distribution = new TDistribution(n - 2);
        return 2d * (1.0 - distribution.cumulativeProbability(
                    FastMath.abs(getSlope()) / getSlopeStdErr()));
    }


    // ---------------------Private methods-----------------------------------

                if (i == j) {
                    out[i][j] = 0d;
                } else {
                    double r = correlationMatrix.getEntry(i, j);
                    double t = FastMath.abs(r * FastMath.sqrt((nObs - 2)/(1 - r * r)));
                    out[i][j] = 2 * tDistribution.cumulativeProbability(-t);
                }
            }
        }
        return new BlockRealMatrix(out);
    }

        throws MaxCountExceededException, MathIllegalArgumentException {


        final double t = FastMath.abs(t(m, mu, v, n));
        // pass a null rng to avoid unneeded overhead as we will not sample from this distribution
        final TDistribution distribution = new TDistribution(null, n - 1);
        return 2.0 * distribution.cumulativeProbability(-t);


    }


    /**
     * Computes p-value for 2-sided, 2-sample t-test.

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