Regression Modelling with the Generalized Power Weibull Distribution under Progressive Censoring

The generalized power Weibull (GPW) distribution has recently attracted attention as a flexible model for lifetime data, but existing work has focused mainly on unconditional inference under progressive Type~II censoring, comparing maximum likelihood, maximum product spacing and Bayesian estimation in the two-parameter case without covariates. In practical reliability and survival studies, however, lifetimes are typically influenced by explanatory variables and censoring is often implemented through progressive schemes. In this paper we develop a regression framework based on a scale-extended GPW distribution under right censoring, with particular emphasis on progressive Type~II designs: the individual-specific scale parameter is linked to covariates via a log-linear model, while the shape parameters are common across units. We derive the likelihood under non-informative censoring, obtain maximum likelihood estimators and their asymptotic covariance matrix, propose maximum product spacing estimators based on transformed uniform variables, and develop a Bayesian version with gamma priors on the shape parameters and a multivariate normal prior on the regression coefficients, estimated via a Metropolis–Hastings-within-Gibbs sampler. A Monte Carlo study examines finite-sample performance across sample sizes, censoring levels and covariate configurations, and a real data analysis with covariates shows that the GPW regression model can outperform classical Weibull and log-normal regression, extending the scope of the GPW family from unconditional modelling to a flexible regression tool for censored lifetime data.