A class of prediction regions for a future upper record interval based on a type-II censored sample from the exponential distribution is presented in this paper. The best prediction region for is then determined by solving a constrained nonlinear optimization problem. The objective function is the area of the prediction region and the constraints are related to the desired confidence level. According to our approach, it suffices to simultaneously solve four nonlinear equations for deriving the prediction region with minimal area. To show the usefulness of our results, we present a simulation study. Three practical studies regarding times between consecutive telephone calls, lifetimes to breakdown of insulating fluids and annual rainfalls recorded at Los Angeles Civic Center are provided for comparing conservative and optimal prediction regions. In most cases, the reduction in area is appreciable. Finally, some applications and extensions are also pointed out.

中文翻译：

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未来指数记录间隔的最佳预测区域

本文提出了一类基于来自指数分布的 II 型截尾样本的未来上记录区间的预测区域。然后通过求解受约束的非线性优化问题来确定 的最佳预测区域。目标函数是预测区域的面积，约束与期望的置信水平有关。根据我们的方法，同时求解四个非线性方程就足以导出具有最小面积的预测区域。为了显示我们的结果的有用性，我们提出了一项模拟研究。提供了三项关于连续电话之间的时间间隔、绝缘流体分解的寿命和洛杉矶市政中心记录的年降雨量的实际研究，用于比较保守和最佳预测区域。在大多数情况下，面积的减少是可观的。最后，还指出了一些应用和扩展。