Given a pair of non-negative random variables $X$ and $Y$, we introduce a class of nonparametric tests for the null hypothesis that $X$ dominates $Y$ in the total time on test order. Critical values are determined using bootstrap-based inference, and the tests are shown to be consistent. The same approach is used to construct tests for the excess wealth order. As a byproduct, we also obtain a class of goodness-of-fit tests for the NBUE family of distributions.

翻译：给定一对非负随机变量$X$和$Y$，我们提出了一类非参数检验方法，用于检验原假设$X$在总检验时间序下优于$Y$。通过基于Bootstrap的推断确定临界值，并证明该检验具有一致性。相同方法被用于构建超额财富序的检验。作为副产品，我们还获得了一类针对NBUE分布族的拟合优度检验。