Classical and Bayesian Parameter Estimation for Generalised Exponential Competing Risks Models Under Improved Adaptive Type-II Progressive Censoring

Competing-risks models play an important role in reliability and survival analysis because failures often arise from several latent causes acting simultaneously. In this paper, we study a two-cause independent competing-risks model in which the latent lifetimes follow the generalised exponential distribution under the improved adaptive Type-II progressive censoring scheme. The proposed framework aims to estimate the model parameters together with the reliability and hazard-rate functions using both classical and Bayesian inference. The frequentist analysis develops maximum likelihood estimators and approximate confidence intervals based on asymptotic theory, whereas the Bayesian analysis employs independent Gamma priors, squared-error loss, and a Metropolis–Hastings algorithm to obtain posterior estimates and highest posterior density credible intervals. An extensive Monte Carlo simulation study is conducted to investigate their finite-sample performance under different censoring schemes, threshold settings, and sample sizes. Finally, two real competing-risks datasets are analysed to illustrate the practical applicability of the proposed methodology and to demonstrate that the generalised exponential competing-risks model provides a competitive alternative for reliability and survival data analysis.