A Flexible Bounded Distribution: Information Measures and Lifetime Data Analysis

This article introduces the Fréchet log-logistic distribution (FLD) model, which offers a notable, bounded, and flexible distribution for modeling increasing and bathtub shapes failure rate phenomena. Compared to well-known distributions like Weibull and Fréchet distributions, the proposed FLD model provides a more adaptable solution to lifetime data modeling. Various mathematical and statistical characteristics of the model, including the hazard function, percentile function, moment generating function, entropy, and characterization, are considered. Real-life data applications of the FLD model are also explored using four data sets, and the results show that the proposed model is a viable alternative to existing lifetime probability models.