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 X k : n is DRHR (IUPL), so are X k - 1 : n , X k : n + 1 , and X k - 1 : n - 1 where X k : n denotes the k -th order statistic of a random sample of size n . It is shown that if the n -th upper k -record R n ( k ) is DRHR then so is R n - 1 ( k ) . Further, we show that DRHR property passes from n -th upper record R n to R n ( k ) .