Third Order Likelihood Inference in the Generalized Exponential Distribution under Progressive Type II Censoring

We consider likelihood inference in the generalized exponential distribution based on progressively type II censored data. The usual likelihood inference procedures do not exist in closed form and therefore large sample likelihood results are often employed for making inference about the distribution parameters and related quantities. However, due to cost and time restrictions, the samples in applied work are usually small and. Therefore, the accuracy of the first order large sample likelihood methods is usually not sufficient. Therefore, higher order asymptotic likelihood methods are needed because they are expected to provide more accurate inferences with small samples. Fraser and Reid (1995) and Fraser et al. (1999) developed a general technique for obtaining third order likelihood inference procedures. In this paper, we employ their technique to develop third-order likelihood inference procedures for the parameters of the generalized exponential distribution based on progressively type II censored data. Specifically, we considered the likelihood ratio test and its third order refinements. We investigated the performance of the intervals based on the likelihood ratio test and its refinements using simulation techniques. Wald intervals were included in the study too. The comparison is based on the extent of the achievement of the nominal confidence levels of the intervals. The results showed that great accuracy can be achieved by the third order methods, especially for small sample sizes. We investigated the power performance of likelihood procedures. A real data example is given to illustrate the results