The beta regression model (BRM) is a popular and widely applied modeling approach, especially when dealing with data bounded within the interval (0, 1). It has been used extensively in various fields, including chemistry, environmental science, medicine, and biology. BRM aims to estimate unknown model parameters, typically achieved using the maximum likelihood estimator (MLE). However, MLE is not without limitations. It can be highly sensitive to multicollinearity and outliers, which can distort coefficient estimates, lead to misleading conclusions, and inflate variance, ultimately increasing the mean squared error (MSE). To address these challenges, this study proposed new robust estimators for BRM that incorporated robust modified ridge-type estimators. These estimators were specifically designed to reduce the adverse effects of multicollinearity and outliers. Their performance was theoretically compared to that of the traditional MLE and robust ridge estimators. In addition, an extensive simulation study was carried out in various scenarios to evaluate their effectiveness. Both theoretical comparisons and simulation results demonstrated the clear advantages of the proposed robust estimators in managing multicollinearity and handling outliers. To further validate the findings, the estimators were applied to real-world data from breast cancer patients. The results confirmed that the proposed robust estimators offer greater robustness and reliability compared to MLE and robust ridge methods. These findings highlighted the practical importance of using robust estimation techniques to improve the accuracy and dependability of BRMs, particularly in empirical research involving highly multicollinear and outlier data.

This paper develops classical and Bayesian inferential procedures for progressively Type-Ⅱ censored competing-risks data when the latent failure times follow the Gompertz-Lindley distribution. Maximum likelihood estimators are derived for the model parameters, and asymptotic confidence intervals are constructed using the observed information matrix. Bayesian estimation is carried out under squared error, LINEX, and generalized entropy loss functions using both the Tierney–Kadane approximation and Markov chain Monte Carlo methods. An extensive Monte Carlo simulation study is conducted to assess the finite-sample behavior of the proposed estimators under different sample sizes and progressive censoring schemes. The numerical results show that Bayesian procedures generally outperform the corresponding maximum likelihood estimators, particularly in small and moderately censored samples. A real-data application involving heart-disease patients demonstrates that the Gompertz-Lindley model provides a satisfactory fit and serves as a flexible alternative for competing-risks lifetime data.

Accelerated life tests play a vital role in reliability analysis, especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition. Among these tests, progressive-stress accelerated life tests (PSALT) allow for continuous changes in applied stress. Additionally, the generalized progressive hybrid censoring (GPHC) scheme has attracted significant attention in reliability and survival analysis, particularly for handling censored data in accelerated testing. It has been applied to various failure models, including competing risks and step-stress models. However, despite its growing relevance, a notable gap remains in the literature regarding the application of GPHC in PSALT models. This paper addresses that gap by studying PSALT under a GPHC scheme with binomial removal. Specifically, it considers lifetimes following the quasi-Xgamma distribution. Model parameters are estimated using both maximum likelihood and Bayesian methods under gamma priors. Interval estimation is provided through approximate confidence intervals, bootstrap methods, and Bayesian credible intervals. Bayesian estimators are derived under squared error and entropy loss functions, using informative priors in simulation and non-informative priors in real data applications. A simulation study is conducted to evaluate various censoring schemes, with coverage probabilities and interval widths assessed via Monte Carlo simulations. Additionally, Bayesian predictive estimates and intervals are presented. The proposed methodology is illustrated through the analysis of two real-world accelerated life test datasets.