A note on reversed hazard rate of order statistics and record values

The reversed hazard rate is an important measure to study the lifetime random variable in reliability theory, survival analysis and stochastic modeling. In the present paper, we study the decreasing reversed hazard rate (DRHR) property of order statistics and record values. Some properties of order statistics related to the increasing uncertainty in past life (IUPL) class have also been studied. We show that if Xk:nXk:n is DRHR (IUPL), so are Xk-1:n,Xk:n+1Xk-1:n,Xk:n+1, and Xk-1:n-1Xk-1:n-1 where Xk:nXk:n denotes the kk-th order statistic of a random sample of size nn. It is shown that if the nn-th upper kk-record Rn(k) is DRHR then so is Rn-1(k). Further, we show that DRHR property passes from nn-th upper record RnRn to Rn(k).