Comparative Performance of Burr Type XII 3P, Dagum Type I 3P and Log-Logistic 3P Distributions in Modeling Ozone (O₃), PM₁₀ and PM₂.₅ Concentrations

This study investigates the suitability of three parameters continuous probability distributions-Burr Type XII 3P, Dagum Type I 3P and Log-Logistic 3P-in modeling secondary air pollutants: ozone (O₃), particulate matters (PM₁₀ and PM₂.₅) in Visakhapatnam, an urban region having rapid industrialization. By employing rigorous statistical techniques including maximum likelihood estimation (MLE) and bootstrapping, we estimate distribution parameters and validate model fit through diagnostic plots-skewness vs. kurtosis, P-P and Q-Q plots as well as goodness-of-fit test-statistics, such as Kolmogorov-Smirnov(KS), Anderson-Darling(AD) and Cramér von Mises(CvM) tests. Additional, performance metrics including Akaike information criterion(AIC), Bayesian information criterion(BIC), evaluation metrics like mean absolute error(MAE), mean absolute percentage error(MAPE), mean squared error(MSE), root mean squared error(RMSE) and coefficient of determination(R²) and cross-validation, were also applied to ensure model robustness. Results indicate that the Burr Type XII 3P distribution most effectively models the high variability and skewed nature of O₃ concentrations, while the Dagum Type I 3P distribution provides the best fit for PM₁₀ and both Burr Type XII 3P and Log-Logistic 3P distributions are suitable for PM₂.₅. These findings offer new insights into the behavior of secondary pollutants, supporting the development of robust air quality monitoring frameworks. R software facilitated all numerical analyses and visualizations of data suited to environmental data modeling.