Pitman closeness of current records for location-scale families

Abstract

In this paper, the largest and the smallest observations are considered, at the time when<br><br>a new record of either kind (upper or lower) occurs based on a sequence of independent<br><br>random variables with identical continuous distributions. These statistics are referred to<br><br>as current upper and lower records, respectively, in the statistical literature. We derive<br><br>expressions for the Pitman closeness of current records to a common population parameter<br><br>and then apply these results to location-scale families of distributions with a special<br><br>emphasis on the estimation of quantiles. In the case of symmetric distributions, we show<br><br>that this criterion possesses some symmetry properties. Exact expressions are derived<br><br>for the Pitman closeness probabilities in the case of Uniform (