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We consider three- and four-level atomic lasers that are either incoherently(unidirectionally) or coherently (bidirectionally) pumped, the single-modecavity being resonant with the laser transition. The intra-cavity Fano factorand the photo-current spectral density are evaluated on the basis of rateequations.  According to that approach, fluctuations are caused by jumps in active anddetecting atoms. The algebra is considerably simpler than the one required byQuantum-Optics treatments.  Whenever a comparison can be made, the expressions obtained coincide. Theconditions under which the output light exhibits sub-Poissonian statistics areconsidered in detail. Analytical results, based on linearization, are verifiedby comparison with Monte Carlo simulations. An essentially exhaustiveinvestigation of sub-Poissonian light generation by three- and four-level atomslasers has been performed. Only special forms were reported earlier.Comment: 9 pages, 7 figures, RevTeX

Rate-equation approach to atomic-laser light statistics