Truncated Exponentiated Weibull-G Family: Theory, Inference, and Modelling of Complete and Hybrid Censored Data

Abstract

In this paper, the truncated exponentiated Weibull-G family is introduced, and its core analytical properties are developed: the density, hazard rate function (hrf), moments, reliability measures, entropy functionals, and selected characterizations. The exponential, Rayleigh, and Lindley baselines serve to illustrate the generator. The proposed family generates flexible models capable of accommodating both symmetric and asymmetric data across varying levels of kurtosis. Its hrfadmits a wide range of shapes, including monotone and non-monotone behaviour increasing, decreasing, bathtub, unimodal, J-shaped, inverse-J-shaped, and others. Estimation is investigated under complete observation and Type-I hybrid censoring through a reproducible Monte Carlo experiment comprising48000 independently generated datasets: four parameter configurations, four sample sizes, three observation regimes, and 1000 replications per design cell. Maximum likelihood and a fixed-prior posterior mode in log-parameter coordinates are assessed throughout, with maximum product spacing evaluated separately for complete samples. Beyond bias and root mean square error, cumulative distribution function recovery, boundary solutions, the availability and conditional coverage of observed-information confidence intervals are examined. The results distinguish useful distributional recovery from persistent identifiability difficulties for individual parameters, particularly under censoring with Bayesian analysis. To test the flexibility of the new class, a lifetime data is analyzed using the exponential-baseline model and compared with three explicitly selected reference distributions, using information criteria and refitted parametric-bootstrap Kolmogorov--Smirnov p-values. The findings illustrate flexible fitting and provide a transparent assessment of point estimation and uncertainty.