Generalized Alpha Power Inverted Weibull Distribution: Application of Air Pollution in Kathmandu, Nepal

A novel probability distribution, the Generalized Alpha Power Inverted Weibull (GAPIW) distribution, is derived from the generalization of the $$\alpha$$ α -power family and compounded with the inverted Weibull distribution. The researchers looked into a lot of different sub-models and found important properties of the GAPIW distribution such as, quantile function, median, mode, moments, mean residual lifetime, and stress-strength reliability. The estimation of distribution parameters was carried out through maximum likelihood estimation methods. To gain insights into the characteristics of the GAPIW distribution, the study applied it to the analysis of air pollution data, specifically PM2.5, PM10, and TSP data from multiple stations in the Kathmandu Valley. Notably, the findings indicate that air quality in these areas was significantly worse during winter than in other seasons. Also, the ratio (PM2.5/PM10) of particulate matter is higher, indicating air pollution from anthropogenesis particles in the Valley. The results demonstrate that the GAPIW distribution is validated through different diagrammatic representations, such as P-P plots, Q-Q plots, and mathematical calculations like the K-S test. The findings reveal that, on average, only three days per month or one month per year predict air pollution levels below the threshold in the Kathmandu Valley. Furthermore, compared to others $$\alpha$$ α -power family of distribution available in the literature, the proposed GAPIW distribution stands as a viable alternative model for assessing and understanding air pollution data and related environmental data. This research has the potential to make valuable contributions to the field of environmental science and air quality monitoring.