Inference for a general family of exponentiated distributions under ranked set sampling with partially observed complementary competing risks data

Ranked set sampling (RSS) acts as an efficient way for collecting failure information due to its ability of saving testing time and cost, and this paper discusses statistical inference for complementary competing risks model under a modified RSS scheme called the maximum ranked set sampling procedure with unequal samples (MRSSU). When the lifetimes of causes of failure are characterized by a general family of exponentiated distributions with partially observed failure causes, parameter estimation is explored from classical likelihood and Bayesian approaches. Existence and uniqueness of maximum likelihood estimators for model parameters are established, and approximate confidence intervals are constructed in consequence. With respect to general flexible priors, Bayes point and interval estimates are constructed, and associated Monte-Carlo sampling is proposed for complex posterior computation. In addition, when there is extra restriction information available, likelihood and Bayes estimates are also proposed in this regard. Extensive simulation studies are conducted to investigate the performance of different methods, and a real-life example is carried out to demonstrate the applications of our results.