On the Monotone Behavior of Time Dependent Entropy of Order alpha

In this paper we study some monotone behavior of the residual (past) entropy of order . 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 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 of (n−k+1)-out-of-n systems and record values are derived. Some results on the residual (past) entropy of order of equilibrium distributions are also obtained.