Stochastic comparisons of record values based on their relative aging

TL;DR

This paper investigates stochastic orderings of record values based on their aging properties, providing conditions under which higher-order records age faster or slower, with applications to hazard rate comparisons.

Contribution

It introduces new stochastic ordering results for record values based on their aging properties, including conditions for relative hazard and reversed hazard rate comparisons.

Findings

mth upper record ages faster than nth when m > n

Relative hazard rate orderings depend on distributional conditions

Reversed hazard rate of mth lower record decreases faster for larger m

Abstract

In this paper we examine some relative orderings of upper and lower records. It is shown that if m > n, the mth upper record ages faster than the nth 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 mth upper record arisen from a continuous distribution ages faster in terms of the relative hazard rate than the nth upper record arisen from another continuous distribution. It is also shown that the reversed hazard rate of the mth lower record decreases faster than the reversed hazard rate of the nth 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.