Classical and Bayesian inference for progressively censored competing risks data under the Gompertz-Lindley model

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.