The use of unmanned aerial vehicle base stations (UAV-BSs) as airborne base stations has recently gained great attention. In this paper, we model a network of UAV-BSs as a Poisson point process (PPP) operating at a certain altitude above the ground users. We adopt an air-to-ground (A2G) channel model that incorporates line-of-sight (LoS) and non-line-of-sight (NLoS) propagation. Thus, UAV-BSs can be decomposed into two independent inhomogeneous PPPs. Under the assumption that NLoS and LoS channels experience Rayleigh and Nakagami-m fading, respectively, we derive approximations for the coverage probability and average achievable rate, and show that these approximations match the simulations with negligible errors. Numerical simulations have shown that the coverage probability and average achievable rate decrease as the height of the UAV-BSs increases.