Nonparametric confidence and tolerance intervals from record values data

Abstract

In a number of situations only observations that exceed or only those that fall below the current extreme value are recorded. Examples include meteorology, hydrology, athletic events and mining. Industrial stress testing is also an example in which only items that are weaker than all the observed items are destroyed. In this paper, it is shown that, how record values can be used to provide distribution-free confidence intervals for population quantiles and tolerance intervals. We provide some tables that help one choose the appropriate record values and present a numerical example. Also universal upper bounds for the expectation of the length of the confidence intervals are derived. The results may be of interest in situation where only record values are stored.