Distribution of the Mahalanobis distance. The box histograms present the distribution of the Mahalanobis distance of the simulations with respect to the mean. The blue curve plots the theoretical χ² distribution for the given degrees of freedom, and the red vertical line presents the Mahalanobis distance of the observation with respect to mean. The generally good fit of the theoretical curve with the histogram of the simulations for all resolutions lends credibility to the validity of the statistical tests in the chosen regimes.