In this study, a new weighted version of the inverse Rayleigh distribution based on two different weight functions is introduced. Some statistical and reliability properties of the introduced distribution including the moments, moment generating function, entropy measures (i.e., Shannon and R´enyi) and survival and hazard rate functions are derived. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. So, a numerical method has been required to compute maximum likelihood estimates. Finally, the daily mean wind speed data set has been analysed to show the usability of the new weighted inverse Rayleigh distribution.

The increasing population and industrialization are the reasons for environmental and air pollution around the world. Air pollution is a major threat, especially to human health, both biological and economic. Therefore, determining the properties of air pollutants is very important for researchers and practitioners working in this field. In this study, the statistical distributions of some air pollutants are determined using the Gumbel, Weibull, generalized Pareto, log-normal, gamma, Rayleigh, and inverse Weibull distributions. The data was obtained from stations Boyabat and Merkez stations in Sinop province in 2017. The Kolmo-Gorov–Smirnov test was used to determine the underlying distributions of the air pollution data. Then we use the root mean square error and coefficient of determination criteria to determine which distribution better fits the air pollution data. Finally, numerical results have shown that the generalized Pareto distribution demonstrates the best overall modeling performance, followed by log-normal and inverse Weibull distributions.

Photovoltaic (PV) power generation plays a critical role in the global transition toward sustainable energy systems. However, accurate PV power forecasting remains challenging due to the non-stationary nature of PV power time series and the presence of structural zeros. Most existing studies rely on parametric models or treat zero inflation as a secondary issue. In this study, a hybrid hurdle modeling framework is implemented to explicitly account for both structural zeros and continuous positive power values through a two-part structure. The zero component is modeled using Bayesian logistic regression (BLR), random forest classifier (RFC), and support vector classifier (SVC). The positive values are analyzed using the parametric models Gamma regression (GR), Log-normal regression (LNR), and Weibull regression (WR) and the non-parametric machine learning (ML) techniques random forest regression (RFR), extreme gradient boosting (XGBoost), and support vector regression (SVR). The proposed framework is validated using the target variable active power (AP, kW) based on a real-world data from a 110 kWe (129.6 kWp) PV plant located in Çaycuma, Zonguldak, Türkiye. Four metrics were used to compare the predictive performances of the models: mean squared error (MSE), mean absolute (scaled) error (MAE and MASE), and the coefficient of determination ( $$\:{R}^{2}$$ ). Among the 18 distinct hurdle models, the lowest error values and the highest $$\:{R}^{2}$$ were obtained when the positive component was modeled by either RFR, such as BLR-RFR (MSE = 67.425 kW, MAE = 3.974 kW, MASE = 0.615, $$\:{R}^{2}$$ = 0.899) or XGBoost, such as RFC-XGBoost (MSE = 69.252 kW, MAE = 4.075 kW, MASE = 0.630, $$\:{R}^{2}$$ = 0.898). The findings indicate that hybrid modeling approaches where the zero component is modeled using BLR, RFC, or SVC, and the positive component is modeled with either RFR or XGBoost provide a reliable framework for PV power forecasting, when predicting continuous data characterized by excessive structural zeros.

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.