Interval estimation for a Pareto distribution based on a doubly type II censored sample

For a complete sample, Chen [Chen, Z., 1996. Joint confidence region for the parameters of a Pareto distribution. Metrika 44, 191-197] proposed an interval estimation of the parameter [theta] and a joint confidence region of two parameters of a Pareto distribution. When the first r lifetimes and the last s lifetimes out of n inspected items are missing, doubly type II censoring has arisen. Since Chen's method cannot be extended to the doubly type II censored sample case, I proposed another joint confidence region for the two parameters of a Pareto distribution. The interval estimation of parameter [nu] is also given for a doubly type II censored sample. Since the complete sample case (r=0) and the right type II censored sample case (r=s=0) are special cases of doubly type II censored samples, the proposed confidence region should also be appropriate for these two special cases, and thus can be compared with Chen's method based on the area of the confidence region. From the simulation results, it can be found that the proposed method is better than Chen's method in obtaining a smaller confidence area. But the difference in area of the two methods becomes very slight when the sample size becomes larger. In this paper, I also proposed the prediction intervals of the future observation and the ratio of the two future consecutive failure times based on the doubly type II censored sample. Finally, an example is given to illustrate the proposed method.