Estimating the parameter of an exponential distribution under multiply type II hybrid censored sample

There are also situations wherein the removal of units prior to failure is pre-planned in order to reduce the cost or time associated with testing. In this paper, we propose the estimators of the parameters of exponential distribution under multiply type II hybrid censoring scheme. Under classical estimation set up, the maximum product spacings (MPS) method is quite effective and several authors advocated the use of this method as an alternative to maximum likelihood (ML) method, and found that this estimation method provides better estimates than ML estimates in various situations. Therefore, we derive the ML estimator (MLE) and maximum product spacings estimator (MPSE) for the parameter of exponential distribution. Also, we derive the approximate MLEs and approximate MPSEs for the parameter of exponential distribution using Talyor series expansion. And we compare the proposed estimators in the sense of mean squared error (MSE) and bias under multiply type II hybrid censoring scheme. Finally, the validity of the proposed methods are demonstrated by a real data.