Statistical Modeling of PM2.5 Concentrations: Prediction of Extreme Events and Evaluation of Advanced Methods for Air Quality Management

This study analyzes the statistical behavior of PM2.5 concentrations in Brasília using advanced probabilistic and time series modeling to support air quality management and extreme event forecasting. The methods applied include Generalized Extreme Value (GEV) distributions, Bayesian inference with Log-Normal distribution, ARIMA models, and quasi-Gaussian approaches. Model performance was evaluated through statistical metrics such as RMSE, R², and the Approximation Index, with parameter estimation improved using the Metropolis-Hastings algorithm. Results show that the GEV 1 model provides a better fit for lower PM2.5 concentrations, while GEV 2 performs better at predicting extreme events. The log-logistic and log-normal distributions also demonstrated good fit, capturing asymmetry and long-tail behavior typical of environmental data. The ARIMA model identified seasonal patterns and supported short-term forecasts, though its predictive capacity for extreme values was limited. Bayesian inference allowed robust estimation of parameter uncertainties and revealed the non-negligible likelihood of severe pollution events. The study concludes that model selection should depend on the forecasting objective: GEV for extremes, Log-Normal for general variability, and ARIMA for trends and seasonality. The use of MCMC sampling techniques significantly improved model robustness. These findings provide a comprehensive framework for understanding air pollution dynamics and guiding public policy on air quality in urban environments.