Confidence interval estimation of a normal percentile

Percentiles (or quantiles) are ubiquitous in descriptive as well as inferential analyses of data. Many applications in practice involve percentiles from the normal distribution. We consider confidence interval estimation of a normal distribution percentile and study several methods including the ones based on the maximum likelihood and the approximate normality of sample percentiles, that is, order statistics. The nonparametric confidence interval, based on the sign test, is included as a benchmark as it is a simple method and is valid for all continuous distributions. A Bayesian posterior predictive interval is also considered. The performance of the methods is examined in a simulation study via coverage and expected length. Summary and recommendations are given.