Parametric Estimation and Analysis of Lifetime Models with Competing Risks Under Middle-Censored Data

Middle-censoring is a general censoring mechanism. In middle-censoring, the exact lifetimes are observed only for a portion of the units and for others, we can only know the random interval within which the failure occurs. In this study, we focus on statistical inference for middle-censored data with competing risks. The latent failure times are assumed to be independent and follow Burr-XII distributions with distinct parameters. To begin with, we derive the maximum likelihood estimators for the unknown parameters, proving their existence and uniqueness. Additionally, asymptotic confidence intervals are constructed using the observed Fisher information matrix. Furthermore, Bayesian estimates under squared loss function and the corresponding highest posterior density intervals are obtained through the Gibbs sampling method. A simulation study is carried out to assess the performance of all proposed estimators. Lastly, an analysis for a practical dataset is provided to demonstrate the inferential processes developed.