Bayesian inference of the parameters under the generalized power Lindley distribution based on the Hybrid type-II censoring scheme: a simulation study and application

In this paper, we examine the Bayesian inference of the parameters of the generalized power Lindley distribution in the presence of type two hybrid censored data.

In estimating the maximum likelihood of the parameters, given that the estimates cannot be obtained implicitly and do not have a closed form, we use the EM algorithm and use Fisher's information matrix to construct asymptotic confidence intervals. Also, in estimating the parameters of the generalized power Lindley distribution, which we display with EPL in the whole article, we use two Lindley approximation methods and Markov chain Monte Carlo under the error squared loss function. We obtain HPD confidence intervals according to Bayesian estimates. Then we compare two Bayesian methods using simulation studies.

It can be seen that the Monte Carlo method for the three-parameter distribution has less bias and is more consistent than the Bayesian parameter estimates from the Lindley approximation. In distributions with many parameters, the MCMC method provides better estimates than the Lindley approximation, and convergence occurs faster in this case. The MSE estimates in the Lindley approximation, according to Table 2, are much larger than the dispersion of data with a similar sample size from the MCMC method in Table 3. and at the end, we provide an example of real data.

 Given that no study has been conducted so far on the generalized Lindley power distribution in the presence of censored hybrid type II, the findings of this study can be used for future studies.