Java Code Examples for org.apache.commons.math3.distribution.TDistribution#cumulativeProbability()

The following examples show how to use org.apache.commons.math3.distribution.TDistribution#cumulativeProbability() . You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. You may check out the related API usage on the sidebar.
Example 1
Source File: PearsonsCorrelationTest.java    From astor with GNU General Public License v2.0 6 votes vote down vote up 
/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
@Test
public void testStdErrorConsistency() {
    TDistribution tDistribution = new TDistribution(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
Example 2
Source File: PearsonsCorrelationTest.java    From astor with GNU General Public License v2.0 6 votes vote down vote up 
/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
@Test
public void testStdErrorConsistency() {
    TDistribution tDistribution = new TDistribution(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
Example 3
Source File: PearsonsCorrelation.java    From astor with GNU General Public License v2.0 6 votes vote down vote up 
/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() {
    TDistribution tDistribution = new TDistribution(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            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);
}
Example 4
Source File: PearsonsCorrelation.java    From astor with GNU General Public License v2.0 6 votes vote down vote up 
/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * @return matrix of p-values
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if an error occurs estimating probabilities
 */
public RealMatrix getCorrelationPValues() {
    TDistribution tDistribution = new TDistribution(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            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);
}
Example 5
Source File: PearsonsCorrelationTest.java    From astor with GNU General Public License v2.0 6 votes vote down vote up 
/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
@Test
public void testStdErrorConsistency() {
    TDistribution tDistribution = new TDistribution(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
Example 6
Source File: PearsonsCorrelationTest.java    From astor with GNU General Public License v2.0 6 votes vote down vote up 
/**
 * Verify that direct t-tests using standard error estimates are consistent
 * with reported p-values
 */
@Test
public void testStdErrorConsistency() throws Exception {
    TDistribution tDistribution = new TDistribution(45);
    RealMatrix matrix = createRealMatrix(swissData, 47, 5);
    PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
    RealMatrix rValues = corrInstance.getCorrelationMatrix();
    RealMatrix pValues = corrInstance.getCorrelationPValues();
    RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
    for (int i = 0; i < 5; i++) {
        for (int j = 0; j < i; j++) {
            double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
            double p = 2 * (1 - tDistribution.cumulativeProbability(t));
            Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
        }
    }
}
Example 7
Source File: XDataFrameLeastSquares.java    From morpheus-core with Apache License 2.0 5 votes vote down vote up 
/**
 * Computes the T-stats and the P-Value for all regression parameters
 */
private void computeParameterSignificance(RealVector betaVector) {
    try {
        final double residualDF = frame.rows().count() - (regressors.size() + 1);
        final TDistribution distribution = new TDistribution(residualDF);
        final double interceptParam = betaVector.getEntry(0);
        final double interceptStdError = intercept.data().getDouble(0, Field.STD_ERROR);
        final double interceptTStat = interceptParam / interceptStdError;
        final double interceptPValue = distribution.cumulativeProbability(-Math.abs(interceptTStat)) * 2d;
        final double interceptCI = interceptStdError * distribution.inverseCumulativeProbability(1d - alpha / 2d);
        this.intercept.data().setDouble(0, Field.PARAMETER, interceptParam);
        this.intercept.data().setDouble(0, Field.T_STAT, interceptTStat);
        this.intercept.data().setDouble(0, Field.P_VALUE, interceptPValue);
        this.intercept.data().setDouble(0, Field.CI_LOWER, interceptParam - interceptCI);
        this.intercept.data().setDouble(0, Field.CI_UPPER, interceptParam + interceptCI);
        final int offset = hasIntercept() ? 1 : 0;
        for (int i=0; i<regressors.size(); ++i) {
            final C regressor = regressors.get(i);
            final double betaParam = betaVector.getEntry(i + offset);
            final double betaStdError = betas.data().getDouble(regressor, Field.STD_ERROR);
            final double tStat = betaParam / betaStdError;
            final double pValue = distribution.cumulativeProbability(-Math.abs(tStat)) * 2d;
            final double betaCI = betaStdError * distribution.inverseCumulativeProbability(1d - alpha / 2d);
            this.betas.data().setDouble(regressor, Field.PARAMETER, betaParam);
            this.betas.data().setDouble(regressor, Field.T_STAT, tStat);
            this.betas.data().setDouble(regressor, Field.P_VALUE, pValue);
            this.betas.data().setDouble(regressor, Field.CI_LOWER, betaParam - betaCI);
            this.betas.data().setDouble(regressor, Field.CI_UPPER, betaParam + betaCI);
        }
    } catch (Exception ex) {
        throw new DataFrameException("Failed to compute regression coefficient t-stats and p-values", ex);
    }
}
Example 8
Source File: WeightedLeastSquaresRegression.java    From Strata with Apache License 2.0 5 votes vote down vote up 
private LeastSquaresRegressionResult getResultWithStatistics(
    double[][] x, double[][] w, double[] y, double[] betas, double[] yModel,
    DoubleMatrix transpose, DoubleMatrix matrix, boolean useIntercept) {

  double yMean = 0.;
  for (double y1 : y) {
    yMean += y1;
  }
  yMean /= y.length;
  double totalSumOfSquares = 0.;
  double errorSumOfSquares = 0.;
  int n = x.length;
  int k = betas.length;
  double[] residuals = new double[n];
  double[] standardErrorsOfBeta = new double[k];
  double[] tStats = new double[k];
  double[] pValues = new double[k];
  for (int i = 0; i < n; i++) {
    totalSumOfSquares += w[i][i] * (y[i] - yMean) * (y[i] - yMean);
    residuals[i] = y[i] - yModel[i];
    errorSumOfSquares += w[i][i] * residuals[i] * residuals[i];
  }
  double regressionSumOfSquares = totalSumOfSquares - errorSumOfSquares;
  double[][] covarianceBetas = convertArray(ALGEBRA.getInverse(ALGEBRA.multiply(transpose, matrix)).toArray());
  double rSquared = regressionSumOfSquares / totalSumOfSquares;
  double adjustedRSquared = 1. - (1 - rSquared) * (n - 1) / (n - k);
  double meanSquareError = errorSumOfSquares / (n - k);
  TDistribution studentT = new TDistribution(n - k);
  for (int i = 0; i < k; i++) {
    standardErrorsOfBeta[i] = Math.sqrt(meanSquareError * covarianceBetas[i][i]);
    tStats[i] = betas[i] / standardErrorsOfBeta[i];
    pValues[i] = 1 - studentT.cumulativeProbability(Math.abs(tStats[i]));
  }
  return new WeightedLeastSquaresRegressionResult(
      betas, residuals, meanSquareError, standardErrorsOfBeta, rSquared, adjustedRSquared, tStats, pValues, useIntercept);
}
Example 9
Source File: RandomWalkSamplerTest.java    From log-synth with Apache License 2.0 4 votes vote down vote up 
@Test
public void testBasics() throws IOException {
    // this sampler has four variables
    // g1 is gamma distributed with alpha = 0.2, beta = 0.2
    // v1 is unit normal
    // v2 is normal with mean = 0, sd = 2
    // v3 is gamma-normal with dof=2, mean = 0.
    SchemaSampler s = new SchemaSampler(Resources.asCharSource(Resources.getResource("schema015.json"), Charsets.UTF_8).read());

    TDigest tdG1 = new AVLTreeDigest(500);
    TDigest tdG2 = new AVLTreeDigest(500);
    TDigest td1 = new AVLTreeDigest(500);
    TDigest td2 = new AVLTreeDigest(500);
    TDigest td3 = new AVLTreeDigest(500);

    double x1 = 0;
    double x2 = 0;
    double x3 = 0;

    for (int i = 0; i < 1000000; i++) {
        JsonNode r = s.sample();
        tdG1.add(r.get("g1").asDouble());
        tdG2.add(r.get("g2").asDouble());

        double step1 = r.get("v1").get("step").asDouble();
        td1.add(step1);
        x1 += step1;
        assertEquals(x1, r.get("v1").get("value").asDouble(), 0);
        assertEquals(x1, r.get("v1-bare").asDouble(), 0);

        double step2 = r.get("v2").get("step").asDouble();
        td2.add(step2);
        x2 += step2;
        assertEquals(x2, r.get("v2").get("value").asDouble(), 0);

        double step3 = r.get("v3").get("step").asDouble();
        td3.add(step3);
        x3 += step3;
        assertEquals(x3, r.get("v3").get("value").asDouble(), 0);
    }

    // now compare against reference distributions to test accuracy of the observed step distributions
    NormalDistribution normalDistribution = new NormalDistribution();
    GammaDistribution gd1 = new GammaDistribution(0.2, 5);
    GammaDistribution gd2 = new GammaDistribution(1, 1);
    TDistribution tDistribution = new TDistribution(2);
    for (double q : new double[]{0.001, 0.01, 0.1, 0.2, 0.5, 0.8, 0.9, 0.99, 0.99}) {
        double uG1 = gd1.cumulativeProbability(tdG1.quantile(q));
        assertEquals(q, uG1, (1 - q) * q * 10e-2);

        double uG2 = gd2.cumulativeProbability(tdG2.quantile(q));
        assertEquals(q, uG2, (1 - q) * q * 10e-2);

        double u1 = normalDistribution.cumulativeProbability(td1.quantile(q));
        assertEquals(q, u1, (1 - q) * q * 10e-2);

        double u2 = normalDistribution.cumulativeProbability(td2.quantile(q) / 2);
        assertEquals(q, u2, (1 - q) * q * 10e-2);

        double u3 = tDistribution.cumulativeProbability(td3.quantile(q));
        assertEquals(q, u3, (1 - q) * q * 10e-2);
    }
}
Example 10
Source File: PearsonsCorrelation.java    From astor with GNU General Public License v2.0 4 votes vote down vote up 
/**
 * Returns a matrix of p-values associated with the (two-sided) null
 * hypothesis that the corresponding correlation coefficient is zero.
 *
 * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability
 * that a random variable distributed as <code>t<sub>n-2</sub></code> takes
 * a value with absolute value greater than or equal to <br>
 * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p>
 *
 * <p>The values in the matrix are sometimes referred to as the
 * <i>significance</i> of the corresponding correlation coefficients.</p>
 *
 * <p>To use this method, one of the constructors that supply an input
 * matrix must have been used to create this instance.</p>
 *
 * @return matrix of p-values
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if an error occurs estimating probabilities
 * @throws NullPointerException if this instance was created with no data
 */
public RealMatrix getCorrelationPValues() {
    TDistribution tDistribution = new TDistribution(nObs - 2);
    int nVars = correlationMatrix.getColumnDimension();
    double[][] out = new double[nVars][nVars];
    for (int i = 0; i < nVars; i++) {
        for (int j = 0; j < nVars; j++) {
            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);
}
Example 11
Source File: TTest.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Computes p-value for 2-sided, 1-sample t-test.
 *
 * @param m sample mean
 * @param mu constant to test against
 * @param v sample variance
 * @param n sample n
 * @return p-value
 * @throws MaxCountExceededException if an error occurs computing the p-value
 */
protected double tTest(final double m, final double mu,
                       final double v, final double n)
    throws MaxCountExceededException {

    double t = FastMath.abs(t(m, mu, v, n));
    TDistribution distribution = new TDistribution(n - 1);
    return 2.0 * distribution.cumulativeProbability(-t);

}
Example 12
Source File: TTest.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Computes p-value for 2-sided, 2-sample t-test.
 * <p>
 * Does not assume subpopulation variances are equal. Degrees of freedom
 * are estimated from the data.</p>
 *
 * @param m1 first sample mean
 * @param m2 second sample mean
 * @param v1 first sample variance
 * @param v2 second sample variance
 * @param n1 first sample n
 * @param n2 second sample n
 * @return p-value
 * @throws MaxCountExceededException if an error occurs computing the p-value
 */
protected double tTest(final double m1, final double m2,
                       final double v1, final double v2,
                       final double n1, final double n2)
    throws MaxCountExceededException {

    final double t = FastMath.abs(t(m1, m2, v1, v2, n1, n2));
    final double degreesOfFreedom = df(v1, v2, n1, n2);
    TDistribution distribution = new TDistribution(degreesOfFreedom);
    return 2.0 * distribution.cumulativeProbability(-t);

}
Example 13
Source File: TTest.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Computes p-value for 2-sided, 2-sample t-test.
 * <p>
 * Does not assume subpopulation variances are equal. Degrees of freedom
 * are estimated from the data.</p>
 *
 * @param m1 first sample mean
 * @param m2 second sample mean
 * @param v1 first sample variance
 * @param v2 second sample variance
 * @param n1 first sample n
 * @param n2 second sample n
 * @return p-value
 * @throws MaxCountExceededException if an error occurs computing the p-value
 */
protected double tTest(final double m1, final double m2,
                       final double v1, final double v2,
                       final double n1, final double n2)
    throws MaxCountExceededException {

    final double t = FastMath.abs(t(m1, m2, v1, v2, n1, n2));
    final double degreesOfFreedom = df(v1, v2, n1, n2);
    TDistribution distribution = new TDistribution(degreesOfFreedom);
    return 2.0 * distribution.cumulativeProbability(-t);

}
Example 14
Source File: TTest.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Computes p-value for 2-sided, 2-sample t-test.
 * <p>
 * Does not assume subpopulation variances are equal. Degrees of freedom
 * are estimated from the data.</p>
 *
 * @param m1 first sample mean
 * @param m2 second sample mean
 * @param v1 first sample variance
 * @param v2 second sample variance
 * @param n1 first sample n
 * @param n2 second sample n
 * @return p-value
 * @throws MaxCountExceededException if an error occurs computing the p-value
 * @throws NotStrictlyPositiveException if the estimated degrees of freedom is not
 * strictly positive
 */
protected double tTest(final double m1, final double m2,
                       final double v1, final double v2,
                       final double n1, final double n2)
    throws MaxCountExceededException, NotStrictlyPositiveException {

    final double t = FastMath.abs(t(m1, m2, v1, v2, n1, n2));
    final double degreesOfFreedom = df(v1, v2, n1, n2);
    TDistribution distribution = new TDistribution(degreesOfFreedom);
    return 2.0 * distribution.cumulativeProbability(-t);

}
Example 15
Source File: TTest.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Computes p-value for 2-sided, 2-sample t-test.
 * <p>
 * Does not assume subpopulation variances are equal. Degrees of freedom
 * are estimated from the data.</p>
 *
 * @param m1 first sample mean
 * @param m2 second sample mean
 * @param v1 first sample variance
 * @param v2 second sample variance
 * @param n1 first sample n
 * @param n2 second sample n
 * @return p-value
 * @throws MaxCountExceededException if an error occurs computing the p-value
 */
protected double tTest(final double m1, final double m2,
                       final double v1, final double v2,
                       final double n1, final double n2)
    throws MaxCountExceededException {

    final double t = FastMath.abs(t(m1, m2, v1, v2, n1, n2));
    final double degreesOfFreedom = df(v1, v2, n1, n2);
    TDistribution distribution = new TDistribution(degreesOfFreedom);
    return 2.0 * distribution.cumulativeProbability(-t);

}
Example 16
Source File: SimpleRegression.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Returns the significance level of the slope (equiv) correlation.
 * <p>
 * Specifically, the returned value is the smallest <code>alpha</code>
 * such that the slope confidence interval with significance level
 * equal to <code>alpha</code> does not include <code>0</code>.
 * On regression output, this is often denoted <code>Prob(|t| > 0)</code>
 * </p><p>
 * <strong>Usage Note</strong>:<br>
 * The validity of this statistic depends on the assumption that the
 * observations included in the model are drawn from a
 * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html">
 * Bivariate Normal Distribution</a>.</p>
 * <p>
 * If there are fewer that <strong>three</strong> observations in the
 * model, or if there is no variation in x, this returns
 * <code>Double.NaN</code>.</p>
 *
 * @return significance level for slope/correlation
 * @throws org.apache.commons.math3.exception.MaxCountExceededException
 * if the significance level can not be computed.
 */
public double getSignificance() {
    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()));
}
Example 17
Source File: TTest.java    From astor with GNU General Public License v2.0 3 votes vote down vote up 
/**
 * Computes p-value for 2-sided, 1-sample t-test.
 *
 * @param m sample mean
 * @param mu constant to test against
 * @param v sample variance
 * @param n sample n
 * @return p-value
 * @throws MaxCountExceededException if an error occurs computing the p-value
 * @throws MathIllegalArgumentException if n is not greater than 1
 */
protected double tTest(final double m, final double mu,
                       final double v, final double n)
    throws MaxCountExceededException, MathIllegalArgumentException {

    double t = FastMath.abs(t(m, mu, v, n));
    TDistribution distribution = new TDistribution(n - 1);
    return 2.0 * distribution.cumulativeProbability(-t);

}