Advancing statistical modelling for complex data with the inverse power induced Bilal distribution

This paper presents a novel probability distribution termed the inverse power induced Bilal distribution (IPIBD). The model is created using the inverse power transformation method. The proposed distribution has a unimodal and right-skewed density. Its hazard rate can be increasing, decreasing, or inverted bathtub-shaped. Several properties of the model are derived. The parameters of the IPIBD were estimated using fifteen different methods. The performance of the estimators was evaluated through simulation studies under different parameter values and sample sizes. The results show that all methods produce stable and reliable estimates. The model is applied to three real-world datasets from different fields and compared with eleven competing distributions using the Akaike information criterion, Bayesian information criterion, and the Kolmogorov–Smirnov statistic, together with other goodness-of-fit measures. The proposed IPIBD consistently provided the best overall fit across the three datasets, demonstrating its effectiveness in modelling complex right-skewed data.