In the present paper, two pivotal statistics are suggested to construct prediction intervals of future observations from the exponential and Pareto distributions in the context of ordered ranked set sample. Our study encompasses two cases. The first case, when the sample size is assumed to be fixed and the second case when the sample size is assumed to be a positive integer-valued random variable. In addition to deriving explicit forms for the distribution functions of the two pivotal statistics, we consider some special cases for the random size of the sample. Moreover, a simulation study is carried out to assess the efficiency of the suggested methods. Finally, an example representing lifetime data is analyzed.

在本文中，建议使用两个关键统计量来在有序排序集样本的背景下从指数分布和帕累托分布构建未来观测值的预测区间。我们的研究包括两个案例。第一种情况，假设样本量是固定的，第二种情况，假设样本量是正整数值随机变量。除了推导出两个关键统计量的分布函数的显式形式外，我们还考虑了样本随机大小的一些特殊情况。此外，还进行了模拟研究以评估所建议方法的效率。最后，分析了一个表示生命周期数据的示例。