Wu utilized the general weighted moments estimator (GWMEs) of the scale parameter of the one-parameter exponential distribution to construct the prediction intervals of the future observations under multiply type II censoring. Since two-parameter exponential distribution has better application for fitting data than one-parameter exponential distribution, Wu proposed the general weighted moments estimator (GWMEs) of the scale parameter for two-parameter exponential distribution and claimed that the proposed estimator outperforms the other 14 estimators including 12 weighted moments estimators proposed by Wu and Yang and approximate maximum likelihood estimator (AMLE) by Balakrishnan and the best linear unbiased estimator (BLUE) by Balasubramanian and Balakrishnan in terms of the exact mean squared errors (MSEs) in most cases. For two-parameter exponential distribution, we use the GWMEs to construct the pivotal quantities for the use of the prediction intervals of future observation. At last, one real life example is given to demonstrate the prediction intervals based on the GWMEs.
