We investigate the statistical properties of two single-mode dye-laser
models - the colored-loss-noise model and the colored-gain-noise mode
l. Analytic expressions of the probability, the mean and the variance
of the steady-state laser in tensity are obtained through the unified
expansion theory [Phys. Rev. A43 (1991) 700]. By comparison we find th
at when the cavity decay rate for the electric field is large and the
pump parameter ao is small, the differences of the results of the two
laser models are small. Otherwise, the differences are large. And the
correlation time of the noise has very obvious influence on the result
s of the two models.