Until recently, the general circulation numerical models ran at resolutions at which the convection was subgrid, and thus, the convection required parameterization. Even if today the resolution of these models has increased such that the deep convection is not fully subgrid, the dry and shallow convection still require parameterization. These parameterization schemes usually assume that in every grid box of the numerical model the convection occupies a very small fractional area, with different schemes describing different types of convection. However, at the present resolutions these assumptions become unrealistic, and thus, new parameterizations need to be developed. For this reason, unified parameterization schemes have been formulated in the recent years. A unified parameterization means either a scheme which is capable to run at any resolution, or a scheme that is able to capture all types of convection (dry, shallow and deep). Although important steps have been made in the recent years towards unified parameterizations, no complete parameterizations have yet been proposed. In this talk, I aim to show how such a complete parameterization could be formulated if one assumes generic convective plumes with stochastic closures.