Distribution-free confidence intervals for quantile intervals based on current records

Suppose we know the combined number of upper and lower records and the current values of the lower and the upper records. Then, it is shown how various exact non-parametric confidence intervals can be constructed based on this information. Such intervals are exact and distribution-free in that the corresponding coverage probabilities are known exactly without any assumption about the parent distribution other than that its distribution function is continuous. Distribution-free outer and inner confidence intervals are obtained for quantile intervals based on current records. An exact expression for the confidence coefficient of these outer and inner confidence intervals are derived. Upper and lower confidence limits for quantile differences are obtained. A data set representing the record values of average July temperatures in Neuenburg, Switzerland, is used to illustrate the results.