A Novel Version of the Arcsine–Rayleigh Distribution with Entropy Measures, Statistical Inference, and Applications

This paper presents a new distribution on the unit interval, named the Unit Arcsine–Rayleigh distribution (UASRD), which is the result of the exponential transformation of the Arcsine–Rayleigh distribution. The model suggested is versatile and can be used in modeling limited reliability and proportion data. Entropy-based measures are also studied to determine the uncertainty and information content of the proposed model and further explain the probabilistic nature of the proposed model and its potential applicability in information-theoretic and reliability tasks. These findings demonstrate the utility of the suggested model in the study of the limited data in the context of information theory. Basic statistical characteristics are derived, such as cumulative and density functions, quantile function, reliability and hazard functions, and ordinary moments. Estimation of parameters is obtained through approaches of maximum likelihood and maximum product spacing and Bayesian estimation of parameters. The performance of the estimators is also assessed by a Monte Carlo simulation study, and the application of real data shows the utility of the proposed model to the analysis of bounded data.