A New Canonical Type II Unitary Weibull–H Family of Distributions with Applications to Lifetime, Reliability, and Survival Data

Selecting an appropriate statistical model to describe lifetime data with heterogeneous characteristics poses a considerable challenge due to the diverse distributional features exhibited by real-world datasets. One effective way to address this challenge is to develop flexible families of distributions capable of generating numerous member distributions. In this paper, the Transformed–Transformer framework is employed to introduce a new and more flexible class of continuous distributions, referred to as the Canonical Type II Unitary Weibull–H family. To illustrate the flexibility of the proposed family, four representative sub-models are derived. Among them, the Canonical Type II Unitary Weibull–Chen distribution is selected for a comprehensive theoretical and empirical investigation. The general properties of the proposed Canonical Type II Unitary Weibull–H family are established, while a detailed study of the Canonical Type II Unitary Weibull–Chen distribution is provided, including mixture representations, the quantile function, moments, probability-weighted moments, Rényi entropy, and order statistics. Moreover, five classical estimation methods, namely maximum likelihood, least squares, weighted least squares, maximum product spacing, and Cramér–von Mises estimation, are employed to estimate the model parameters. In addition, an extensive Monte Carlo simulation study is conducted to evaluate and compare the finite-sample performance of the different estimators. Finally, the practical usefulness of the proposed distribution is illustrated through the analysis of four real-world datasets representing waiting time, biomedical, survival, and reliability applications. Comparisons based on several goodness-of-fit criteria demonstrate that the Canonical Type II Unitary Weibull–Chen distribution provides a competitive and, in many cases, superior fit relative to several well-established competing models.