In this paper, the statistical behabiors are analysed for an arbitrary paraxial beam with two dimentional distribution in the transverse section, and the propagation parameters are obtained for the equivalent Gaussian beam which can describe the statistical behaviors of the paraxial beam. The results in reference can be derived from the conclusions in this paper by using the concept of “embedded Gaussian beam”. This results can be used in the geometrical description for the propagation of a paraxial beam.