Regression models for time-to-event data are widely used in clinical and reliability studies, particularly in the presence of censoring. In this context, the Weibull regression model provides a flexible alternative to the proportional hazards model, allowing for a fully specified survival function and interpretable measures of treatment effects. However, inference based on classical test statistics may be unreliable in small or moderate samples. In this paper, we derive closed-form approximations for the non-null asymptotic distributions of the likelihood ratio, Wald, score, and gradient tests under Pitman alternatives in Weibull regression models for censored data. These results facilitate analytical evaluation of local power and provide a basis for comparing the performance of the four tests. The proposed approximations are assessed through simulation studies, which highlight their accuracy in moderate-to-large samples and illustrate the impact of censoring and model complexity. An application is presented to the design of Phase Ⅱ clinical trials to demonstrate how derived power functions can be used to estimate sample sizes. The results provide a computationally efficient tool for power analysis in censored Weibull regression models, although their use in practice should be complemented with simulation-based validation in small-sample or high-censoring scenarios.

In this article, we introduced an extension of the chi-square distribution by employing a slash-type methodology that enhanced the weight of the right tail, thereby producing a heavy-tailed distribution. We explored two different representations of the proposed distribution and examined several of its key properties, such as the mode, cumulative distribution function, reliability and hazard functions, moments, and the skewness and kurtosis coefficients. Additionally, we demonstrated that the classical chi-square distribution was a special case of our proposed model. Parameter estimation was carried out using both the method of moments and the maximum likelihood estimation, the latter via the expectation-maximization (EM) algorithm. A simulation study was conducted to evaluate the performance of parameter recovery. Finally, we applied the new distribution to a wind speed dataset, showing that it provided a good fit, particularly in the presence of extreme values.

We introduced the Gauss hypergeometric Gleser (GHG) distribution, a novel extension of the Gleser (G) distribution that unifies families of Gleser distributions. We studied their representations and some basic properties and showed that the GHG distribution is heavy-tailed. The maximum likelihood method is used for parameter estimation, and the Fisher information matrix derived. We assessed the performance of the maximum likelihood estimators via Monte Carlo simulations. Moreover, we present applications to two data sets in which the GHG distribution shows a better fit than other known distributions.