Exact Likelihood Inference for Parameter of Exponential Distribution under Combined Generalized Progressive Hybrid Censoring Scheme

Recently, the generalized type I progressive hybrid censoring scheme (GenT1PrHyCS) and generalized type II progressive hybrid censoring scheme (GenT2PrHyCS) have become quite popular in reliability studies. These two type censoring schemes are very complex due to the large number of parameters used to specify the censoring procedure. Therefore, in this paper, we consider a more general and more complex new censoring scheme. Also, we consider the exponential distribution(ExpD) and derive an expression for the density function of the MLE. We prove the exact distribution of the maximum likelihood estimator (MLE) and conditional moment generating function (CondMGF) of the MLE for the mean of the ExpD under a new censoring scheme. We then derive the exact confidence intervals (ConfItv) for the mean of the ExpD under a new censoring scheme. Finally, we present an example to explain the methods of inference derived for this paper. From the example data, it can be seen that PDF of MLE for ExpD under new censoring scheme is almost symmetrical.