Review on construction confidence interval for difference quantiles of two independent normal distributions

In this paper, the problem of making inferences on the difference between quantiles of two independent normal distributions is addressed. In this regard, we apply a parametric bootstrap (PB) approach, and a method of variance estimates recovery (MOVER) to construct confidence intervals for the difference between quantiles. The coverage probability and average length of the proposed approaches are compared through Monte Carlo simulations. Simulation results show that our proposed MOVER confidence interval can be recommended generally for different sample sizes and number of groups. The interval estimation methods are applied to a real world case study to show their performance in life data analysis