  We consider three- and four-level atomic lasers that are either incoherently
(unidirectionally) or coherently (bidirectionally) pumped, the single-mode
cavity being resonant with the laser transition. The intra-cavity Fano factor
and the photo-current spectral density are evaluated on the basis of rate
equations.
  According to that approach, fluctuations are caused by jumps in active and
detecting atoms. The algebra is considerably simpler than the one required by
Quantum-Optics treatments.
  Whenever a comparison can be made, the expressions obtained coincide. The
conditions under which the output light exhibits sub-Poissonian statistics are
considered in detail. Analytical results, based on linearization, are verified
by comparison with Monte Carlo simulations. An essentially exhaustive
investigation of sub-Poissonian light generation by three- and four-level atoms
lasers has been performed. Only special forms were reported earlier.
