Reliability estimation under type-II censored data from the generalized Bilal distribution

The main object of this article is the estimation of the unknown population parameters
and the reliability function for the generalized Bilal model under type-II censored data.
Both maximum likelihood and Bayesian estimates are considered. In the Bayesian
framework, although we have discussed mainly the squared error loss function, any
other loss function can easily be considered. Gibb’s sampling procedure is used to
draw Markov Chain Monte Carlo (MCMC) samples, which have been used to compute
the Bayes estimates and also to construct their corresponding credible intervals with
the help of two different importance sampling techniques. A simulation study is carried
out to examine the accuracy of the resulting Bayesian estimates and compare them
with their corresponding maximum likelihood estimates. Application to a real data set
is considered for the sake of illustration