Stochastic comparisons of record values based on their relative aging

Abstract

In this paper we examine some relative orderings of upper and lower records. It is shown that if \(m>n\), the \(m\)th upper record ages faster than the \(n\)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 \(m\)th upper record arisen from a continuous distribution ages faster in terms of the relative hazard rate than the \(n\) th upper record arisen from another continuous distribution. It is also shown that the reversed hazard rate of the \(m\)th lower record decreases faster than the reversed hazard rate of the \(n\)th lower record, when \(m>n\). Preservation property of the relative reversed hazard rate order at lower record values is investigated. Several examples are presented to examine the results.