On the mean residual waiting time of records

Abstract

Abstract In this paper, we examine the mean residual waiting time of record values from a sequence of identically independent random variables with a common continuous distribution F. Under the condition that the (m+1)-st shock has not arrived by time t>0, we obtain a simplified expression for the mean residual waiting time of the (n+1)-st shock. We investigate some monotonicity and aging properties for the mean residual waiting time of records. Further, it is shown that the underlying distribution function F can be recovered via the functional relationships between the mean residual waiting times of records.