New Two-Parameter Weibull–Lindley Distribution‎: ‎Mathematical Properties‎, ‎Simulation‎, ‎and Applications

This study proposes the New Two-Parameter Weibull–Lindley Distribution (NTPWLD), a flexible lifetime model generated through a transformation of a one-parameter baseline survival function. Owing to its general structure, the NTPWLD accommodates diverse hazard rate shapes, including increasing, decreasing, and bathtub forms, and captures both light- and heavy-tailed behaviors relevant to survival analysis, engineering reliability, and biomedical applications. The work provides a full mathematical treatment of the distribution, deriving closed-form expressions for its density, distribution, survival, hazard, and quantile functions, along with ordinary and incomplete moments, the moment generating function, mean deviations, and Rényi entropy. Several reliability measures, such as mean residual life and stress–strength reliability, are also obtained. Parameter estimation is examined under various inferential approaches, with particular focus on maximum likelihood estimation. A Monte Carlo simulation study shows that the maximum likelihood estimator performs well across settings, displaying low bias, stability, and consistency. To incorporate uncertainty in lifetime data, fuzzy reliability measures are constructed using Zadeh’s extension principle and α-cut techniques. Applications to two real datasets demonstrate that the NTPWLD provides superior goodness-of-fit compared with several competing models based on AIC, BIC, AICC, and −۲ log L, highlighting its practical value in both precise and fuzzy reliability environments.‎

کلیدواژه ها:

Weibull–Lindley distribution ، reliability analysis ، Parameter estimation ، Simulation