Shannon information properties of the Endpoints of Record Coverage

Abstract

This paper addresses the largest and the smallest observations, at the times when a<br><br>new record of either kind (upper or lower) occurs, which are it called the current<br><br>upper and lower record, respectively. We examine the entropy properties of these<br><br>statistics, especially the difference between entropy of upper and lower bounds of<br><br>record coverage. The results are presented for some common parametric families<br><br>of distributions. Several upper and lower bounds, in terms of the entropy of parent<br><br>distribution, for the entropy of current records are obtained. It is shown that mutual<br><br>information, as well as Kullback–Leibler distance between the endpoints of record<br><br>coverage, Kullback–Leibler distance between data distribution, and current records,<br><br>are all distribution-free.