Modeling precipitation and insurance data using  type II exponentiated half-logistic exponential distribution

This study introduces and rigorously investigates the novel three-parameter Type II Exponentiated Half-Logistic Exponential (TIIEHLEx) distribution, designed to offer enhanced flexibility for modeling positive-valued data in fields such as hydrology and risk analysis. We first establish the model's theoretical foundation, demonstrating that its probability density function (PDF) is versatile and that its hazard rate function can capture non-monotone risk patterns (bathtub, inverted bathtub, IHR, and DHR), positioning it favorably against models with restricted hazard shapes. A comprehensive simulation study evaluating fourteen non-Bayesian estimation methods confirmed that the Minimum Spacing Absolute Distance Estimator (MSADE) consistently provided the most accurate and reliable parameter estimates (lowest Bias, MSE, and MRE). Applying the TIIEHLEx model to two distinct real-world datasets—March Precipitation and Annual Insurance and Financial Services data—we demonstrated its empirical superiority, as evidenced by the highest Kolmogorov-Smirnov p-values and lowest information criteria compared to several competitor models. This work validates the TIIEHLEx distribution as a highly versatile and robust tool for reliable modeling and parameter estimation of complex data structures.