Comparing Parameter Estimation Methods for Daily Maximum PM10 Data in the Presence of Anomalously Large Observations

Real-world datasets may contain unusually large observations whose origin cannot always be clearly identified. When such observations are present, selecting an appropriate estimation method becomes particularly important because they may substantially influence distribution fitting and parameter estimation. In this study, daily maximum PM10 data recorded at the Erfelek Station in Sinop (Türkiye) during 2025 were analyzed, and several probability distributions were fitted. The lognormal (LN) distribution provided the best overall fit according to the goodness-of-fit criteria. To evaluate the sensitivity of estimation methods to unusually large observations, contamination scenarios were considered, and the performances of Weighted Least Absolute Deviation-1 (WLAD-1), Weighted Least Absolute Deviation-2 (WLAD-2), Least Absolute Deviation (LAD), Least Squares (LS), Least Median of Squares (LMS), and Maximum Likelihood (ML) were compared. The results indicate that WLAD-2 and LMS are the most robust estimators, remaining unaffected by outliers across all contamination levels. WLAD-1, LAD, and LS are also only negligibly affected, whereas the ML estimator becomes increasingly sensitive as the contamination level increases. Contamination also affects exceedance probabilities and return periods, with substantially greater changes observed for the ML estimator than for the remaining estimators.