THE HAZARD RATE AND THE REVERSED HAZARD RATE ORDERS, WITH APPLICATIONS TO ORDER STATISTICS

ASOK K. NANDA^{1} AND MOSHE SHAKED^{2}

1Department of Mathematics, Indian Institute of Technology, Kharagpur 721 302, India 2Department of Mathematics, University of Arizona, Tucson, AZ 85721, U.S.A.

(Received March 13, 2000; revised June 23, 2000)

Abstract. In this paper we first point out a simple observation that can be used successfully in order to translate results about the hazard rate order into results about the reversed hazard rate order. Using it, we derive some interesting new results which compare order statistics in the hazard and in the reversed hazard rate orders; as well as in the usual stochastic order. We also simplify proofs of some known results involving the reversed hazard rate order. Finally, a few further applications of the observation are given.

Key words and phrases: Stochastic orders, k-out-of-n systems.