We consider the problem of modeling the number of times that an air quality standard is exceeded in a certain period of time. We assume that the number of times the threshold is exceeded takes place according to a non-homogeneous Poisson process (NHPP) with the mean function modeled by the generalized gamma distribution. We consider models with and without change-points. When the presence of change-points is assumed, we have none, one, two or three change-points, depending on the data set. We use the Bayesian approach, where the posterior summaries of interest are obtained using standard Markov Chain Monte Carlo (MCMC) methods. We also discuss the use of different prior distributions for the parameters of the models, with an analysis of the convergence of the Gibbs sampling algorithm and sensitivity for the choice of different priors. To illustrate the proposed method we consider simulated data and a pollution data set from of a region of Mexico City.