It is very important to study the occurrence of high levels of particulate matter due to the potential harm to people's health and to the environment. In the present work we use a non-homogeneous Poisson model to analyse the rate of exceedances of particulate matter with diameter smaller that 2.5 microns (PM${}_{2.5}$). Models with and without change-points are considered and they are applied to data from Bogota, Colombia, and Mexico City, Mexico. Results show that whereas in Bogota larger particles pose a more serious problem, in Mexico City, even though nowadays levels are more controlled, in the recent past PM${}_{2.5}$ were the ones causing serious problems.

由于对人类健康和环境的潜在危害，研究高浓度颗粒物的发生非常重要。在目前的工作中，我们使用非均匀泊松模型来分析直径小于 2.5 微米的颗粒物（PM${}_{2.5}$）。考虑了有和没有变化点的模型，并将它们应用于来自哥伦比亚波哥大和墨西哥墨西哥城的数据。结果表明，尽管在波哥大，较大的颗粒会造成更严重的问题，但在墨西哥城，尽管现在的水平受到了更多控制，但在最近过去的 PM${}_{2.5}$是那些造成严重问题的人。