Estimation of the PDF and the CDF of the two-parameter exponential distribution for type-II censored sample

The article addresses different estimators of the probability density function and the cumulative distribution function for the two-parameter exponential distribution for type-II censored sample. Following estimation methods are considered: maximum likelihood estimator, uniformly minimum variance unbiased estimator and plug-in uniformly minimum variance unbiased estimator. Analysis of real data sets are performed to compare the performances of the proposed methods of estimation. The maximum likelihood estimators of the PDF and the CDF are performing better in mean squared error sense. In case of unknown location and known scale parameter, plug-in uniformly minimum variance unbiased estimator is performing better.