Examples of org.apache.commons.math3.stat.inference.KolmogorovSmirnovTest

Package org.apache.commons.math3.stat.inference

Examples of org.apache.commons.math3.stat.inference.KolmogorovSmirnovTest

org.apache.commons.math3.exception.util.ExceptionContext
kipedia.org/wiki/Kolmogorov-Smirnov_test"> Kolmogorov-Smirnov (K-S) test for equality of continuous distributions.
The K-S test uses a statistic based on the maximum deviation of the empirical distribution of sample data points from the distribution expected under the null hypothesis. For one-sample tests evaluating the null hypothesis that a set of sample data points follow a given distribution, the test statistic is \(D_n=\sup_x |F_n(x)-F(x)|\), where \(F\) is the expected distribution and \(F_n\) is the empirical distribution of the \(n\) sample data points. The distribution of \(D_n\) is estimated using a method based on [1] with certain quick decisions for extreme values given in [2].

Two-sample tests are also supported, evaluating the null hypothesis that the two samples {@code x} and {@code y} come from the same underlying distribution. In this case, the teststatistic is \(D_{n,m}=\sup_t | F_n(t)-F_m(t)|\) where \(n\) is the length of {@code x}, \(m\) is the length of {@code y}, \(F_n\) is the empirical distribution that puts mass \(1/n\) at each of the values in {@code x} and \(F_m\) is the empirical distribution of the {@code y} values. Thedefault 2-sample test method, {@link #kolmogorovSmirnovTest(double[],double[])} works asfollows:
- For very small samples (where the product of the sample sizes is less than {@value #SMALL_SAMPLE_PRODUCT}), the exact distribution is used to compute the p-value for the 2-sample test.
- For mid-size samples (product of sample sizes greater than or equal to {@value #SMALL_SAMPLE_PRODUCT} but less than {@value #LARGE_SAMPLE_PRODUCT}), Monte Carlo simulation is used to compute the p-value. The simulation randomly generates partitions of \(m + n\) into an \(m\)-set and an \(n\)-set and reports the proportion that give \(D\) values exceeding the observed value.
- When the product of the sample sizes exceeds {@value #LARGE_SAMPLE_PRODUCT}, the asymptotic distribution of \(D_{n,m}\) is used. See {@link #approximateP(double,int,int)} for details onthe approximation.
In the two-sample case, \(D_{n,m}\) has a discrete distribution. This makes the p-value associated with the null hypothesis \(H_0 : D_{n,m} \ge d \) differ from \(H_0 : D_{n,m} > d \) by the mass of the observed value \(d\). To distinguish these, the two-sample tests use a boolean {@code strict} parameter. This parameter is ignored for large samples.

The methods used by the 2-sample default implementation are also exposed directly:
- {@link #exactP(double,int,int,boolean)} computes exact 2-sample p-values
- {@link #monteCarloP(double,int,int,boolean,int)} computes 2-sample p-values by MonteCarlo simulation
- {@link #approximateP(double,int,int)} uses the asymptotic distribution The {@code boolean}arguments in the first two methods allow the probability used to estimate the p-value to be expressed using strict or non-strict inequality. See {@link #kolmogorovSmirnovTest(double[],double[],boolean)}.
References:
- [1] Evaluating Kolmogorov's Distribution by George Marsaglia, Wai Wan Tsang, and Jingbo Wang
- [2] Computing the Two-Sided Kolmogorov-Smirnov Distribution by Richard Simard and Pierre L'Ecuyer
Note that [1] contains an error in computing h, refer to MATH-437 for details.
@since 3.3

                          double abs,
                          ConvergenceChecker<UnivariatePointValuePair> checker) {
        super(checker);


        if (rel < MIN_RELATIVE_TOLERANCE) {
            throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);
        }
        if (abs <= 0) {
            throw new NotStrictlyPositiveException(abs);
        }

View Full Code Here

    @Override
    public double inverseCumulativeProbability(double p) throws OutOfRangeException {
        double ret;


        if (p < 0.0 || p > 1.0) {
            throw new OutOfRangeException(p, 0.0, 1.0);
        } else if (p == 1.0) {
            ret = Double.POSITIVE_INFINITY;
        } else {
            ret = -mean * FastMath.log(1.0 - p);
        }

View Full Code Here

        if (lo >= hi) {
            throw new NumberIsTooLargeException(lo, hi, false);
        }
        if (init < lo ||
            init > hi) {
            throw new OutOfRangeException(init, lo, hi);
        }


        lower = lo;
        upper = hi;
        start = init;

View Full Code Here


    @Override
    public double inverseCumulativeProbability(double p)
        throws OutOfRangeException {
        if (p < 0 || p > 1) {
            throw new OutOfRangeException(p, 0, 1);
        }
        if (p == 0) {
            return a;
        }
        if (p == 1) {

View Full Code Here

        /**
         * {@inheritDoc}
         * @throws TooManyEvaluationsException.
         */
        public void trigger(int max) {
            throw new TooManyEvaluationsException(max);
        }

View Full Code Here

    protected void incrementEvaluationCount()
        throws TooManyEvaluationsException {
        try {
            evaluations.incrementCount();
        } catch (MaxCountExceededException e) {
            throw new TooManyEvaluationsException(e.getMax());
        }
    }

View Full Code Here

        /**
         * {@inheritDoc}
         * @throws TooManyIterationsException.
         */
        public void trigger(int max) {
            throw new TooManyIterationsException(max);
        }

View Full Code Here

                                              double threshold) {
        super(wrong, threshold, false);
        this.index = index;
        this.threshold = threshold;


        final ExceptionContext context = getContext();
        context.addMessage(LocalizedFormats.NOT_POSITIVE_DEFINITE_MATRIX);
        context.addMessage(LocalizedFormats.ARRAY_ELEMENT, wrong, index);
    }

View Full Code Here

            final double t = x.dotProduct(z);
            final double epsa = (s + MACH_PREC) * CBRT_MACH_PREC;
            if (FastMath.abs(s - t) > epsa) {
                final NonSelfAdjointOperatorException e;
                e = new NonSelfAdjointOperatorException();
                final ExceptionContext context = e.getContext();
                context.setValue(SymmLQ.OPERATOR, l);
                context.setValue(SymmLQ.VECTOR1, x);
                context.setValue(SymmLQ.VECTOR2, y);
                context.setValue(SymmLQ.THRESHOLD, Double.valueOf(epsa));
                throw e;
            }
        }

View Full Code Here

         */
        private static void throwNPDLOException(final RealLinearOperator l,
            final RealVector v) throws NonPositiveDefiniteOperatorException {
            final NonPositiveDefiniteOperatorException e;
            e = new NonPositiveDefiniteOperatorException();
            final ExceptionContext context = e.getContext();
            context.setValue(OPERATOR, l);
            context.setValue(VECTOR, v);
            throw e;
        }

View Full Code Here

0 1 2 3 4 5 6 7 8 9

TOP

Related Classes of org.apache.commons.math3.stat.inference.KolmogorovSmirnovTest

org.apache.commons.math3.analysis.differentiation.DerivativeStructure

org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction

org.apache.commons.math3.analysis.function.HarmonicOscillator

org.apache.commons.math3.analysis.function.Sin

org.apache.commons.math3.analysis.function.Sinc

org.apache.commons.math3.analysis.MultivariateFunction

org.apache.commons.math3.analysis.QuinticFunction

org.apache.commons.math3.analysis.solvers.BrentSolver

org.apache.commons.math3.analysis.UnivariateFunction

org.apache.commons.math3.complex.Complex

All source code are property of their respective owners. Java is a trademark of Sun Microsystems, Inc and owned by ORACLE Inc. Contact coftware#gmail.com.