For the purpose of deriving an appropriate distribution defined over the bounded unit interval ( 0 , 1 ) , this paper introduces a new extension of the standard unit Rayleigh distribution called the unit power Rayleigh distribution (UPRD). However, numerous traditional unit lifetime distributions have restricted flexibility for modeling bounded data with different skewness and hazard rate behaviors. Theoretical investigations into probability density, reliability, and the hazard rate function of the UPRD demonstrate that the UPRD provides a flexible and effective framework for modeling reliability and survival data. To further explore its statistical behavior, several key properties including the stochastic ordering, the quintile function, raw and incomplete moments, moment generating function, along with related measures like Shannon entropy, Lorentz and Bonferroni curve functions, and stress–strength reliability are analytically derived. Parameter estimation for the UPRD is performed using the maximum likelihood, the least squares, weighted least square, and Cramer-von Misses estimation methods. The obtained estimates are evaluated through a simulation study, using average values, absolute biases, mean square errors, and standard error, which indicates that the estimation methods are adequate and efficient for estimating the model parameters. The applicability of the proposed UPRD distribution is demonstrated using two real engineering reliability datasets. Compared with several related unit distributions, the results clearly show that the UPRD provides the best fit and is the most suitable model for this type of data.
Al-Olaimat et al. (Fri,) studied this question.