Interval estimation for the two-parameter exponential distribution under progressive censoring

The interval estimation of the scale parameter and the joint confidence region of the parameters of two-parameter exponential distribution under Type II progressive censoring is proposed. In addition, the simulation study for the performance of all proposed pivotal quantities is done in this paper. The criteria of minimum confidence length and minimum confidence area are used to obtain the optimal estimation. The predictive intervals of the future observation and the future interarrival times based on the Type II progressive censored sample are also provided. One biometrical example is also given to illustrate the proposed methods.