Every intensive human activity, such as industrial processes, agriculture, transport, or heat and electricity generation from fossil fuels, is simultaneously a source of pollution. Air pollution represents a serious health risk and causes significant environmental damage. In particular, long-term exposure to high levels of particulate matter PM10 and PM2.5 can cause heart disease, stroke, lung disease, or lung cancer. Therefore, it is necessary to monitor and predict the concentrations of air pollutants to implement short-term as well as long-term actions to prevent health-risky situations. The main objective of this study is to determine the best probability distribution for modeling the particulate matter PM10 and PM2.5 concentrations in the city of Trenčín, Slovakia. The modeled dataset, consisting of daily average concentrations of PM10 and PM2.5 measured from January 1, 2017, to December 31, 2024, was fitted with extreme value distributions, namely lognormal, gamma, Gumbel, loglogistic, Weibull, and exponentiated Weibull distributions. The exponentiated Weibull probability distribution has not yet been fitted to such a dataset. To identify the best-fitting distribution, five performance indicators were applied. The root mean squared error (RMSE), the coefficient of determination (R2), and the prediction accuracy (PA) were used to determine which distribution better fits the air pollution data. The goodness-of-fit of the probability density functions to the data was evaluated using the Kolmogorov-Smirnov and Anderson-Darling tests. The Weibull distribution achieved the worst performance; on the other hand, the exponentiated Weibull distribution ranked among the top three best distributions. However, all the proposed distributions can be used to model the particulate matter PM10 and PM2.5.

Acknowledgement: KEGA 025ŽU-4/2024 Implementation of new didactic tools to increase the quality of mathematics teaching in the engineering degree at technical universities.