In this paper, the estimation of unknown parameters of Chen distribution
is considered under progressive Type-II censoring in the
presence of competing failure causes. It is assumed that the latent
causes of failures have independent Chen distributions with the
common shape parameter, but different scale parameters. From a
frequentist perspective, the maximum likelihood estimate of parameters
via expectation–maximization (EM) algorithm is obtained. Also,
the expected Fisher information matrix based on the missing information
principle is computed. By using the obtained expected Fisher
information matrix of the MLEs, asymptotic 95% confidence intervals
for the parameters are constructed. We also apply the bootstrap
methods (Bootstrap-p and Bootstrap-t) to construct confidence
intervals. From Bayesian aspect, the Bayes estimates of the unknown
parameters are computed by applying the Markov chain Monte Carlo
(MCMC) procedure, the average length and coverage rate of credible
intervals are also carried out. The Bayes inference is based on the
squared error, LINEX, and general entropy loss functions. The performance
of point estimators and confidence intervals is evaluated
by a simulation study. Finally, a real-life example is considered for
illustrative purposes.