Inference for Generalized Inverted Exponential Distribution Under Progressive Type-I Censoring Scheme in Presence of Competing Risks Model

In this paper, the problem of estimation of the parameters for the GIED based on progressive Type-I censoring scheme in the presence of competing risks model will be considered under Bayesian and non-Bayesian approaches. In this regards, the MLEs, asymptotic confidence intervals and bootstrap confidence interval for the unknown parameters are obtained. The relative risks due to each cause of failure are investigated, where two independent causes of failure are assumed. Also, Bayes estimates and associated HPD credible interval estimates are computed using MCMC by utilizing Metropolis-Hasting algorithm under squared error loss function. A Monte Carlo simulation study will be conducted to compare the performance of the various proposed estimators. Finally, analysis of a real data set is used to illustrate the theoretical results of relative risk, MLE estimates and Bayes estimates at selected schemes of progressively Type-I censored samples under causes of failure follow the assumed distributions.