Confidence intervals for quantiles based on samples of random sizes

On the basis of failure times of a sample of random size N of iid continuous random variables, we consider the estimation problem of population quantiles of the same distribution. Based on order statistics, confidence intervals for quantile intervals are introduced. Confidence intervals for the difference of quantiles are also investigated. Exact expressions for the coverage probabilities of these intervals are derived and computed numerically. A biometric data set representing the duration of remission of 20 Leukemia patients is used to illustrate the results developed here.