The new Weibull–Pareto distribution (NWPD) has recently been proposed as a flexible lifetime model with attractive reliability properties and tractable inference for complete data. Existing work, however, focuses exclusively on univariate settings without covariates and assumes fully observed lifetimes. In many practical applications, survival times are subject to right censoring and depend on individual-level covariates such as age, treatment group, or operating conditions. In this paper we develop a regression framework for right-censored survival data with a new Weibull–Pareto baseline. We embed the NWPD in a parametric regression model by allowing the scale parameter to depend on covariates through a log-linear link. The resulting model enjoys both accelerated failure time (AFT) and proportional hazards (PH) interpretations, while preserving the analytical tractability of the NWPD. We derive the likelihood and score functions for right-censored data, propose maximum likelihood estimation based on numerical optimization, and outline asymptotic inference via the observed information matrix. A Monte Carlo study design is presented to assess finite-sample performance of the estimators under varying sample sizes and censoring levels. We also describe a template for real-data applications, including model diagnostics and comparison with standard Weibull and log-logistic regression models. The proposed framework extends the scope of the NWPD from a purely distributional model to a fully fledged survival regression tool for applied reliability and biomedical studies.
The new Weibull–Pareto distribution (NWPD) has recently been proposed as a flexible lifetime model with attractive reliability properties and tractable inference for complete data. Existing work, however, focuses exclusively on univariate settings without covariates and assumes fully observed lifetimes. In many practical applications, survival times are subject to right censoring and depend on individual-level covariates such as age, treatment group, or operating conditions. In this paper we develop a regression framework for right-censored survival data with a new Weibull–Pareto baseline. We embed the NWPD in a parametric regression model by allowing the scale parameter to depend on covariates through a log-linear link. The resulting model enjoys both accelerated failure time (AFT) and proportional hazards (PH) interpretations, while preserving the analytical tractability of the NWPD. We derive the likelihood and score functions for right-censored data, propose maximum likelihood estimation based on numerical optimization, and outline asymptotic inference via the observed information matrix. A Monte Carlo study design is presented to assess finite-sample performance of the estimators under varying sample sizes and censoring levels. We also describe a template for real-data applications, including model diagnostics and comparison with standard Weibull and log-logistic regression models. The proposed framework extends the scope of the NWPD from a purely distributional model to a fully fledged survival regression tool for applied reliability and biomedical studies.
