Testing the equality of two normal percentiles

Estimation of the percentile of Birnbaum-Saunders distribution and its application to PM2.5 in Northern Thailand

The Birnbaum-Saunders distribution plays a crucial role in statistical analysis, serving as a model for failure time distribution in engineering and the distribution of particulate matter 2.5 (PM2.5) in environmental sciences. When assessing the health risks linked to PM2.5, it is crucial to give significant weight to percentile values, particularly focusing on lower percentiles, as they offer a more precise depiction of exposure levels and potential health hazards for the population. Mean and variance metrics may not fully encapsulate the comprehensive spectrum of risks connected to PM2.5 exposure. Various approaches, including the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach, were employed to establish confidence intervals for the percentile of the Birnbaum-Saunders distribution. To assess the performance of these intervals, Monte Carlo simulations were conducted, evaluating them based on coverage probability and average length. The results demonstrate that the GCI approach is a favorable choice for estimating percentile confidence intervals. In conclusion, this article presents the results of the simulation study and showcases the practical application of these findings in the field of environmental sciences.

Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients

In many applications, comparing the q-quantiles of several normal populations are more advantageous than comparing their means. In this paper, we consider the problem of constructing simultaneous confidence intervals (SCIs) for quantile differences of several heterogeneous normal distributions. To the best of our knowledge, this problem remains unsolved. We propose a novel method for constructing a set of SCI. We propose two new sets of SCI by using the proposed technique and discuss two classic and two simulation-based SCIs. We show that the proposed classic SCIs are conservative for all population parameters configuration. We also show that the simulation-based SCIs have correct coverage probability asymptotically. We then compare these six sets of SCI in terms of average volume and coverage probability via an extensive simulation study. Results show that one of the proposed classic SCI can be recommended. Finally, the proposed methods are illustrated by a real example that is a vitamin D study on colorectal cancer patients.