Nonparametric confidence intervals for quantile intervals and quantile differences based on record statistics

It is shown how various exact nonparametric inferential procedures can be developed based on record statistics. These include confidence intervals for quantiles, tolerance intervals, outer and inner confidence intervals for quantile intervals, and upper and lower confidence limits for quantile differences. These intervals are all 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. A data set representing the records of the annual (July 1–June 30) rainfall at Los Angeles Civic Center is used to illustrate the proposed inferential procedures.