Weighted boundary test: WBOUNDS

The weighted boundary test is calculated in a way similar to the BOUNDS test, but taking into account how far the outliers are from the boundaries $rmax, rmin$ of the reference data. The score is computed as

$$\frac{\sum_{i}{\left(d(X_i)\right)}}{N}$$ (3)

where $N$ is the number of actual data, and $d(X_i)$ is a function of the distance of the $X_i$ value from the reference range, defined as

[IMAGE png] (4)

with $R = (rmax - rmin)$ and $D_x =$ distance of $x$ from the nearest boundary. This computation allows giving less importance to ``near'' outliers and more importance to ``far'' outliers. The default value of $k$, a multiplier of the min-max range, is $1.0$; this can be changed to modify the index sensitivity.

The WBOUNDS score is forced to $0$ if the above computation yields a negative value, for consistency with the other indexes and to keep its meaning in the variable score computation. The actual value can be retrieved through the tests' statistics.