Stochastic comparisons of record values based on their relative aging

In this paper we examine some relative orderings of upper and lower records. It is shown that if \(m>n\) $m>n$ , the \(m\) $m$ th upper record ages faster than the \(n\) $n$ th upper record, where the data sets come from a sequence of independent and identically distributed observations from a continuous distribution. Sufficient conditions are also obtained to see whether the \(m\) $m$ th upper record arisen from a continuous distribution ages faster in terms of the relative hazard rate than the \(n\) $n$ th upper record arisen from another continuous distribution. It is also shown that the reversed hazard rate of the \(m\) $m$ th lower record decreases faster than the reversed hazard rate of the \(n\) $n$ th lower record, when \(m>n\) $m>n$ . Preservation property of the relative reversed hazard rate order at lower record values is investigated. Several examples are presented to examine the results.