Advancing statistical inference through the truncated copoun distribution with engineering applications

This paper introduces the Truncated Copoun (TCpn) distribution, a novel and flexible two-parameter model defined on the unit interval for modeling bounded lifetime data. The proposed distribution accommodates a wide range of shapes, including U-shaped and J-shaped densities and hazard functions, providing greater flexibility than existing bounded models. Key statistical properties are derived in closed form, and model parameters are estimated via maximum likelihood. A Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the estimators, demonstrating improved accuracy and consistency as sample size increases. The practical usefulness of the TCpn distribution is illustrated using two real datasets: Boeing 720 air-conditioning system failure times and polyester fiber tensile strength data. Comparative analysis based on AIC, BIC, CAIC, HQIC, and the Kolmogorov–Smirnov test shows that the TCpn model outperforms several competing distributions. Graphical assessments using P–P and Q–Q plots further confirm the adequacy of the proposed model.