We study the statistical behavior of two out of equilibrium systems. The first one is a quasi-one-dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions. The second one is a one-dimensional spin system with nearest-neighbor interactions also under the influence of an external driving force. Both systems show a dynamical scaling with domain formation. The statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk. We find that the scaling domain size distribution of the gas and the spin systems is well-fitted by the Wigner surmise, which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices. However, the study of the correlation function of the domain edges shows that the statistical behavior of the domains in both gas and spin systems is not completely well-described by a circular orthogonal ensemble, nor it is by other models proposed such as the coalescing random walk and the interacting random walk. Nevertheless, we find that a simple model of independent intervals describes more closely the statistical behavior of the domains formed in these systems.