In this paper, a new probability model is suggested, known as the Unit Linear Failure Rate Distribution (ULFRD), which is used to analyse data expressed on a unit interval (0, 1), e.g., proportions, rates, and normalised indices. The proposed model is a transformation of the classical linear failure rate distribution to finite domains and gives us the opportunity to have shapes with a variety of shapes that can model any hazard rate behaviour, such as bathtub-shaped ones that are common in reliability research. Various fundamental statistical features of the distribution are obtained. The parameter estimation is analysed under Type-II censoring, where maximum likelihood and Bayesian estimations are used. Bayesian estimates are obtained under a symmetric and an asymmetric loss of a Metropolis–Hastings within a Gibbs approximation. The analyses of the estimates’ performance are performed via a simulation study of various sample sizes and censoring plans. Lastly, the generalisability of the proposed model is also demonstrated with two real datasets in the socioeconomic and reliability settings. The findings prove that the ULFRD offers a flexible and competitive alternative to model-bound data.
Al-Moisheer et al. (2026) studied this question.