A Competing Risk Model Based on a Two-Parameter Exponential Family Distribution Under Progressive Type II Censoring

Abstract

AbstractThis chapter presents a competing risk model with two dependent failure causes whose latent failure times are Marshall–Olkin bivariate exponential family distribution that includes Burr XII, Gompertz, and Weibull distributions as special cases. Maximum likelihood estimation and Bayesian estimation methods for the model parameters are discussed. The existence and uniqueness of maximum likelihood estimates are established under some regular conditions for Weibull and Burr XII base distributions, respectively. A Markov-Chain Monte Carlo process is proposed for Bayesian estimation method. Due to the possible flaw of maximum likelihood estimation method, a Monte Carlo simulation study is only conducted to assess the performance of Bayesian estimations for model parameters, tenth percentile, median and ninety percentile lifetimes under square error, absolute error, and LINEX loss functions. A real data set is used for illustration.