  In this article, it is shown that the $C_k$ and $LCm$ variables, recently
introduced as an effective way to discriminate gamma and proton-induced showers
in large wide-field gamma-ray observatories, can be generalised to be used in
arrays of different detectors and variable fill factors. In particular, the
$C_k$ profile discrimination capabilities are evaluated for scintillator and
water Cherenkov detector arrays.
