Abstract In constructing a confidence interval for the mean difference of two independent populations, we may encounter the problem of having a low coverage probability when there are many zeros in the data, and the non-zero values are highly positively skewed. The violation of the normality assumption makes parametric methods inefficient in such cases. In this paper, jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) methods are proposed to construct a nonparametric confidence interval for the mean difference of two independent zero-inflated skewed populations. The JEL and AJEL confidence intervals are compared with the confidence intervals by normal approximation and empirical likelihood proposed by Zhou and Zhou (2005). Simulation studies are performed to assess the new methods. Two real-life datasets are also used as an illustration of the proposed methodologies.

中文翻译：

---

两个零膨胀偏态群体的平均差的 Jackknife 经验似然

摘要 在构建两个独立总体的均值差的置信区间时，可能会遇到数据中零点较多、非零值高度正偏的情况下覆盖概率低的问题。在这种情况下，违反正态性假设会使参数方法效率低下。在本文中，提出了折刀经验似然（JEL）和调整折刀经验似然（AJEL）方法来构建两个独立的零膨胀偏态群体的平均差异的非参数置信区间。将 JEL 和 AJEL 置信区间与 Zhou 和 Zhou (2005) 提出的正态近似和经验似然的置信区间进行比较。进行模拟研究以评估新方法。