Entropy Properties of Certain Record Statistics and Some Characterization Results

In this paper, the largest and the smallest observationsare considered, at the time when a new record of either kind (upper orlower) occurs based on a sequence of independent random variableswith identical continuous distributions. We prove that sequences ofthe residual or past entropy of the current records characterizes Fin the family of continuous distributions. The exponential and theFrechet distributions are characterized through maximizing Shannonentropies of these statistics under some constraint