  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.
