Statistical Modeling of Daily Average Levels of Carbon Monoxide (CO), Sulfur Dioxide (SO2), and Nitric Oxide (NO) in Visakhapatnam Using the Burr-XII Distribution

Abstract

Urban air pollution is a critical global challenge, especially in rapidly industrializing cities, where effective environmental management requires robust probabilistic models. This study evaluates the three parameter Burr-XII distribution for modeling daily average concentrations of carbon monoxide (CO), sulfur dioxide (SO₂), and nitric oxide (NO) in Visakhapatnam, India, using data from January 1st, 2018 to December 31st, 2022. Various statistical tools-such as skewness-kurtosis plots, probability density functions (PDFs), empirical cumulative distribution functions (ECDFs), P-P, and Q-Q plots are employed to assess the model's validity. Maximum Likelihood Estimation (MLE), goodness-of-fit tests (Kolmogorov-Smirnov, Anderson-Darling, and Cramér-von Mises), and model selection criteria like Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) are applied to evaluate the performance of the Burr-XII distribution compared to the Dagum-I and Log-Logistic distributions. Results show that the Burr-XII distribution consistently provides the best fit, demonstrating superior error metrics-mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and the coefficient of determination (R²), excelling in goodness-of-fit and model selection criteria, while showing lower standard errors and better alignment with empirical data, particularly in the tails and extreme values. These findings highlight the robustness of the Burr-XII distribution in capturing the variability and skewness inherent in air pollutant concentrations. The study underscores the potential of the Burr-XII distribution as a reliable tool for air quality modeling, enhancing pollution forecasting and regulatory compliance. By supporting effective environmental monitoring and policy-making, the findings contribute to improved public health protection in urban centers.