Entropy Properties of Certain Record Statistics and Some Characterization Results

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the Frechet distributions are characterized through maximizing Shannon entropies of these statistics under some constraint.