Bootstrap-based tests for the total time on test and the excess wealth orders

Abstract

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 (New Better than Used in Expectation) family of distributions.