New distribution demonstrates enhanced fitting performance in lifetime data analysis, indicating its practical relevance.
In this study, a new unit interval distribution defined on the unit interval is developed through a power transformation approach and termed the Power Unit Haq (PUH) distribution. Several key statistical properties of the new distribution are derived, including incomplete moments, moments, and associated measures, moment generating function, hazard function, mean residual life function, and Rényi entropy. The parameters of the proposed distribution are estimated using five estimation approaches, and their performance is evaluated through extensive Monte Carlo simulations. The flexibility and practical relevance of the new distribution are further demonstrated by utilizing three real datasets-one involving radiation, reactor pump failures, and kidney dialysis patients. The proposed distribution exhibits superior fitting performance compared to established competing unit interval distributions. Additionally, Bayesian estimation of the model parameter is carried out, enhancing the distribution’s applicability for real-world scenarios.
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Alomair et al. (2025) studied this question.
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