  We study the statistics and characteristics of rare intense events in two
types of two dimensional Complex Ginzburg-Landau (CGL) equation based models.
Our numerical simulations show finite amplitude collapse-like solutions which
approach the infinite amplitude solutions of the nonlinear Schr\"{o}dinger
(NLS) equation in an appropriate parameter regime. We also determine the
probability distribution function (PDF) of the amplitude of the CGL solutions,
which is found to be approximately described by a stretched exponential
distribution, $P(|A|) \approx e^{-|A|^\eta}$, where $\eta < 1$. This
non-Gaussian PDF is explained by the nonlinear characteristics of individual
bursts combined with the statistics of bursts. Our results suggest a general
picture in which an incoherent background of weakly interacting waves,
occasionally, `by chance', initiates intense, coherent, self-reinforcing,
highly nonlinear events.
