Stochastic Properties of Residual Life and Inactivity Time at a Random Time

We present sufficient conditions for log-concavity and log-convexity of the residual life and the inactivity time. We also make stochastic comparisons on the residual life and the inactivity time in terms of the failure rate order, the mean residual life order and the usual stochastic order. These results strengthen some conclusions in Li and Zuo [11] Li , X. ; Zuo , M.J. Stochastic comparisons of residual life and inactivity time at a random time . Stochastic Models 2004 , 20 ( 2 ), 229 – 235 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] and Yue and Cao [19] Yue , D. ; Cao , J. Some results on the residual life at random time . Acta. Math. Appl. Sinica. 2000 , 16 , 436 – 443 . [Google Scholar].