Utilizing Unmanned Aerial Vehicles (UAVs) to provide coverage service has a variety of advantages over terrestrial cellular networks. A typical one is that multiple adjacent UAVs can form swarms dynamically to provide stable connection for high populated areas. Due to the random location feature, stochastic geometry tool is used to evaluate their coverage performance. Prior work leveraged Poisson/Binomial and Poisson cluster processes to characterize single-swarm and multi-swarm respectively. These models simplify the analytical procedure at the price of failing to capture heavy-tailed property of UAV numbers in swarms inspired by population density. This leads to underestimated interference impact, inaccurate performance evaluation and insufficient UAV deployments. For this reason, for the first time, we leverage Sibuya and discrete α -stable processes to characterize single-swarm and multi-swarm networks respectively. These two processes have tractable probability generation functionals and capture heavy tail property as well. In addition, we derive the coverage probability under the maximal instantaneous signal-to-interference ratio association policy for both deployments. Finally, simulation results validate our analytical models.