<h3 style="color:#941333">Short methodology description (control limits estimation)</h3>
<p>
A statistical method has been developed to automatically estimate the control limits of any variable based on the shape of  the data distribution tails. The main assumption is that a cluster of points is considered as not belonging to the distribution, i.e. considered outliers or unrealistic values, when they are separated from the main data distribution beyond a certain distance. This distance, the “outlier distance”, is expressed in the corresponding variable units and it should be specific for each data distribution and for each tail.
<p/>
<p>
A convenient procedure to estimate the outlier distance is computing the distance between a pair of specific percentiles characteristic of the corresponding distribution tail. Distributions with long-tails will present larger percentile distances than distributions with short-tails; thus the outlier distance will be larger for the former ones as expected. Once a pair of percentiles is selected and the outlier distance computed, the procedure consists of searching the first gap in the distribution tail large enough to fit the outlier distance. The estimated control limits will be defined by the external side of the fitted outlier distance. An appropriate approach in the outlier distance computation is estimating the percentiles after taking the log10 of the original data distribution. This step exponentially enlarges the contribution of the tails in the percentile estimation, which is essential to correctly incorporate the tail’s shape of long-tail distributions.
<p/>
<p>
In order to get more robust results and minimize the dependency on the specific pair of percentiles selected, a wide range of possible percentiles pairs are used to produce a wide range of outlier distances and thus of control limits. All these estimated control limits are then sorted in a histogram and then the most frequent binned value is the one provided as estimation for the control limits.
<p/>
<p>
Note that this method does not incorporate any physical constraint and thus does not guarantee physical plausibility. It can only be taken as a tool to automatically identify suspicious values of being unrealistic.
<p/>
<p>
A detailed technical report of this method is under publication.
<p/>