A bounded Lindley exponential model with applications to industrial engineering and epidemiological data

The log-Lindley exponential (LLE), a bounded variant of the Lindley exponential distribution, is introduced using the inverse exponential transformation method. The LLE demonstrates significant flexibility, generating novel and well-known distributions with various parameters and providing support, including log-Lindley, Lindley, and two-parameter Lindley distributions, and exhibiting diverse density shapes, including right-skewed, approximately symmetric, left-skewed, decreasing, U-shaped, and increasing, while the hazard rate can be increasing, J-shaped, and bathtub-shaped. We explore several important statistical properties of the LLE model, including moments, entropy, quantile function, actuarial measures, mean residual life function, and stochastic orderings, which enhance its applicability in practical settings. Our study presents nine distinct frequentist strategies for estimating the model's parameters. In addition, the performance of the proposed estimation method is studied and evaluated through extensive numerical simulations. Finally, applications to real-world datasets from industrial engineering and epidemiology reveal the LLE model's practical utility and superiority, with it outperforming other existing models in terms of goodness-of-fit and flexibility.