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

/**
 * 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);
    }
}
 

private static double calcMeanCI(SummaryStatistics stats, double level) {
    try {
        TDistribution tDist = new TDistribution(stats.getN() - 1);
        double critVal = tDist.inverseCumulativeProbability(1.0 - (1 - level) / 2);
        return critVal * stats.getStandardDeviation() / Math.sqrt(stats.getN());
    } catch (MathIllegalArgumentException e) {
        return Double.NaN;
    }
}
 

/**
 * Adapted from https://gist.github.com/gcardone/5536578.
 *
 * @param alpha probability of incorrectly rejecting the null hypothesis (1
 * - confidence_level)
 * @param df degrees of freedom
 * @param n number of observations
 * @param std standard deviation
 * @param mean mean
 * @return array with the confidence interval: [mean - margin of error, mean
 * + margin of error]
 */
public static double[] getConfidenceInterval(final double alpha, final int df, final int n, final double std, final double mean) {
    // Create T Distribution with df degrees of freedom
    TDistribution tDist = new TDistribution(df);
    // Calculate critical value
    double critVal = tDist.inverseCumulativeProbability(1.0 - alpha);
    // Calculate confidence interval
    double ci = critVal * std / Math.sqrt(n);
    double lower = mean - ci;
    double upper = mean + ci;
    double[] interval = new double[]{lower, upper};
    return interval;
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha)
throws OutOfRangeException {
    if (n < 3) {
        return Double.NaN;
    }
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    // No advertised NotStrictlyPositiveException here - will return NaN above
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha) {
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha) {
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha)
throws OutOfRangeException {
    if (n < 3) {
        return Double.NaN;
    }
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    // No advertised NotStrictlyPositiveException here - will return NaN above
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha) {
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha)
throws OutOfRangeException {
    if (n < 3) {
        return Double.NaN;
    }
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    // No advertised NotStrictlyPositiveException here - will return NaN above
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha)
throws OutOfRangeException {
    if (n < 3) {
        return Double.NaN;
    }
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    // No advertised NotStrictlyPositiveException here - will return NaN above
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}
 

/**
 * Returns the half-width of a (100-100*alpha)% confidence interval for
 * the slope estimate.
 * <p>
 * The (100-100*alpha)% confidence interval is </p>
 * <p>
 * <code>(getSlope() - getSlopeConfidenceInterval(),
 * getSlope() + getSlopeConfidenceInterval())</code></p>
 * <p>
 * To request, for example, a 99% confidence interval, use
 * <code>alpha = .01</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>
 * <strong> Preconditions:</strong><ul>
 * <li>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>.
 * </li>
 * <li><code>(0 < alpha < 1)</code>; otherwise an
 * <code>OutOfRangeException</code> is thrown.
 * </li></ul></p>
 *
 * @param alpha the desired significance level
 * @return half-width of 95% confidence interval for the slope estimate
 * @throws OutOfRangeException if the confidence interval can not be computed.
 */
public double getSlopeConfidenceInterval(final double alpha)
throws OutOfRangeException {
    if (n < 3) {
        return Double.NaN;
    }
    if (alpha >= 1 || alpha <= 0) {
        throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL,
                                      alpha, 0, 1);
    }
    // No advertised NotStrictlyPositiveException here - will return NaN above
    TDistribution distribution = new TDistribution(n - 2);
    return getSlopeStdErr() *
        distribution.inverseCumulativeProbability(1d - alpha / 2d);
}