anderson-darling

/**
 * @brief Checks if given points are form a given distribution
 * @param x
 * @param dist distribution name
 * @return A squared
 */
double StatUtils::andersonDarlingTest(Points1D x, const QString &d) {

  // Check point count
  int n = x.size();
  if (n < 25) {
    QString msg = QString("Anderson-Darling: '%1' is too few points for test.");
    logWarning(msg.arg(n));
  }
  if (n >= 1000) {
    QString msg = QString("Anderson-Darling: '%1' is too many points for test. "
                          "Consider for example Kolmogorov-Smirnov test.");
    logWarning(msg.arg(n));
  }

  // Sort data
  qSort(x);

  // Choose distribution
  // NOTE: Adjustment coeficient has to be chosen. The test is most often used
  // in contexts where a family of distributions is being tested, in which case
  // the parameters of that family need to be estimated and account must be
  // taken of this in adjusting either the test-statistic or its critical values
  double adj;
  if (d.compare("normal") == 0 || d.compare("gauss")) {
    adj = 1.0 + (0.75 + 2.25 / n) / n;
    x = normcdf(zscore(x));
  } else {
    logError(QString("Anderson-Darling test for %1 not implemented").arg(d));
    return -1;
  }

  // Check data validity
  for (int i = 0; i < n; i++) {
    if (x[i] < 0.0 || x[i] > 1.0) {
      logError("Anderson-Darling test requires data in CDF form");
      return -1;
    }
  }

  // Calculate data for standard normal CDF
  Points1D data;
  for (int i = 0; i < n; i++) {
    double coef =  2 * (i + 1) - 1;
    double alog = log(x[i]);
    double blog = log(1 - x[n - (i + 1)]);
    data.append(coef * (alog + blog));
  }
  double asq = -n - MathUtils::sum(data) / n;
  return asq * adj;
}
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