kolmogorov-smirnov

/**
 * @brief Performs one sample Kolmogorov-Smirnov test
 * @param x points
 * @param d distribution name ('normal',...)
 * @return probability that points have given distribution
 */
double StatUtils::kolmogorovSmirnovTest(Points1D x, const QString &d) {

  // Calculate size of array and sort it
  int n = x.size();
  qSort(x);

  // Choose distribution
  if (d.compare("normal") == 0 || d.compare("gauss")) {
    x = normcdf(zscore(x));
  } else {
    QString msg = QString("Kolmogorov-Smirnov test for %1 not implemented");
    logError(msg.arg(d));
    return -1;
  }

  // Calculate probability that given sequence of points belong to distribution
  Points1D a1 = MathUtils::div(MathUtils::sequence(0.0, (double) n + 0), n);
  Points1D a2 = MathUtils::div(MathUtils::sequence(1.0, (double) n + 1), n);
  Points1D asub1 = MathUtils::abs(MathUtils::sub(x, a1));
  Points1D asub2 = MathUtils::abs(MathUtils::sub(x, a2));
  double ks = sqrt(n) * MathUtils::max(MathUtils::max(asub1, asub2));
  return 1 - kolmogorovcdf(ks);
}
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