Nonparametric confidence intervals for quantiles and quantile intervals from inversely sampled record breaking data in a multi-sample plan

Abstract

There are a number of situations in which an observation is retained only if it is a record value, which include studies in industrial quality control experiments, destructive stress testing, meteorology, hydrology, seismology, athletic events and mining. When the number of records is fixed in advance, the data are referred to as inversely sampled record-breaking data. In this paper, we study the problems of constructing the nonparametric confidence intervals for quantiles and quantile intervals of the parent distribution based on record data. For a single record-breaking sample, the confidence coefficients of the confidence intervals for the pth quantile cannot exceed p and 1−p, on the basis of upper and lower records, respectively; hence, replication is required. So, we develop the procedure based on k independent record-breaking samples. Various cases have been studied and in each case, the optimal k and the exact nonparametric confidence intervals are obtained, and exact expressions for the confidence coefficients of these confidence intervals are derived. Finally, the results are illustrated by numerical computations.