In a long term evolution (LTE) based cellular network, the mobility management entity (MME) is responsible for non-data signaling between user equipment of multiple base stations in a geographic region and the core network. Thus, the MME residence time (MRT) is a key parameter required to improve the performance of an LTE based cellular network. The impact of various mobility and network scenarios on cell residence time has been studied in the literature. However, the MRT has not been suitably modeled. Hence, in this paper, we consider diverse mobility and network scenarios. For these scenarios, we model the MRT using various probability distributions. We analyze and evaluate the statistical performance of these distributions in modeling MRT. Finally, we show through exhaustive simulations that the Lognormal and Generalized Pareto distributions are best suited to model the MRT for specific network and mobility scenarios. © 2018 IEEE.