We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators.We acknowledge financial support by the MICINN (Spain) and FEDER (EU) through
project FIS2007-60327. L.F.L. is supported by the
JAEPredoc program of CSIC.Peer reviewe