Characterizations Using Entropies of Records in a Geometric Random Record Model

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function $F$, within this set of observations denote the random number of records by $M$. This is called geometric random record model. In this paper, characterizations of $F$ are provided in terms of the subsequences entropies of records conditional on events ${M geq n}$ or ${M = n}$ in a geometric random record model. Characterization results for symmetric distributions are also presented based on entropies of upper and lower records in a random record model.