Some characterization results based on doubly truncated reversed residual lifetime random variable

Abstract

In view of the growing importance of the reversed residual lifetime in reliability anal-<br><br>ysis and stochastic modeling, in this paper, we try to study some of the reliability<br><br>properties of reversed residual lifetime random variable based on doubly truncated<br><br>data and complete the preceding results such as Ruiz and Navarro (1995, 1996),<br><br>Navarro et al. (1998), Nanda et al. (2003), Nair and Sudheesh (2008) and Sudheesh<br><br>and Nair (2010). The monotonicity properties of the doubly truncated reversed resid-<br><br>ual variance and its relations with doubly truncated reversed residual expected value<br><br>and doubly truncated reversed residual coefficient of variation are discussed. Further-<br><br>more, an upper bound for it under some conditions is obtained. We also discuss and<br><br>find the similar results and some characterizations for discrete random ageing, which<br><br>are noticeable in comparing with continuous cases.