Particle velocity distribution function (PVDF) is key to kinetic theory of granular flow. Studies have shown that the PVDFs in gas-solid flow can be Maxwellian, bimodal and/or non-Maxwellian with an overpopulated high-energy tail. In this short communication, topography analysis was carried out to elucidate the mathematical nature of bimodal distribution. It was shown that both of the non-Maxwellian distribution with an overpopulated high-energy tail and the Maxwellian distribution are special cases of bimodal distribution, therefore, bimodal distribution can be used as the starting point of developing a unified kinetic theory for gas-solid flow. Furthermore, the constrained conditions for the transition from bimodal distribution to the non-Maxwellian distribution with an overpopulated high-energy tail were identified. (C) 2018 Elsevier Ltd. All rights reserved.