On the Monotone Behavior of Time Dependent Entropy of Order α

In this paper we study some monotone behavior of the residual (past) entropy of order alpha We prove that, under some relation between the hazard rates (reversed hazard rates) of two distributions functions F and G, when the residual (past) entropy of order alpha of F is decreasing (increasing) then the residual (past) entropy of G is decreasing (increasing). Using this, several conclusions regarding monotone behavior of residual (past) entropy of order a of (n - k+1)out- of-n systems and record values are derived. Some results on the residual (past) entropy of order alpha of equilibrium distributions are also obtained.