Some distributions related to double records in iid sequences

Abstract We are concerned with the appearance of double records (two records in a row) in a sequence of independent and identically distributed (iid) random variables with absolutely continuous distribution, say F . We investigate distributions associated to the position of double records both within the original sequence and among the sequence of records. These distributions are free in the sense that they do not depend on the common distribution F . In fact, these distributions can be obtained by using a connection between iid samples and random permutations. We also study distributions associated to the values of double records. These statistics are not distribution free, so without loss of generality we consider the case in which F is the distribution function of a random variable uniformly distributed in (0, 1). As far as we know these statistics has not been studied before.