Maximum likelihood estimators, EM algorithm, Fisher information matrix, Asymptotic distribution, Optimal censoring scheme, 62N05, 62F10,

The two most popular censoring schemes are type-I and type-II censoring schemes. Hybrid censoring scheme is a mixture of type-I and type-II censoring schemes. In this paper we mainly consider the analysis of hybrid censored data when the lifetime distribution of the individual item is a two-parameter generalized exponential distribution. It is observed that the maximum likelihood estimators can not be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. We obtain the observed Fisher information matrix using the missing information principle and it can be used for constructing the asymptomatic confidence intervals. We also obtain the Bayes estimates of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. One data set has been analyzed for illustrative purposes.

The two most common censoring schemes used in life testing experiments are Type-I and Type-II censoring schemes. Hybrid censoring scheme is mixture of Type-I and Type-II censoring scheme. In this work we consider the estimation of parameters of log-normal distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method. It is observed that the maximum likelihood estimates can not be obtained in closed form. We obtain the maximum likelihood estimates of the unknown parameters using EM algorithm. We also propose approximate maximum likelihood estimates and these can be used as initial estimates for any iterative procedure. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. The method of obtaining optimum censoring scheme is discussed. One data set is analyzed for illustrative purposes.

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Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters can not be obtained in closed form. Lindley's approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process, and we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.

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