Nonparametric confidence and tolerance intervals from record values data

Abstract

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