Estimation for the generalized inverted exponential distribution under adaptive progressive type II hybrid censoring scheme

This paper discusses the point and interval estimation of two parameters of generalized inverted exponential distribution under the adaptive progressive type II hybrid censoring scheme. The maximum likelihood estimators of two parameters have been derived by using Newton-Raphson method and the existence and uniqueness of them have been proved. Furthermore, the asymptotic and transformed confidence intervals of the parameters have been constructed. On the other hand, the Bayesian estimation has been approximated with Lindley and Importance Sampling methods, since there is no explicit solution. Moreover, the highest posterior density credible intervals of two parameters have been established. Then, the proposed approaches have been compared and illustrated through the simulation and actual data of breakdown time of an electrically insulating fluid. Finally, the optimal censoring scheme is suggested via three optimization rules.