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
Saripalli Arun Kumar, Akiri Sridhar, Sarode Rekha, Vasili B. V. Nagarjuna and Ramanaiah
M.
Res. J. Chem. Environ.; Vol. 29(4); 39-56;
doi: https://doi.org/10.25303/294rjce039056; (2025)
Abstract
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.
