AISM 53, 853-864

© 2001 ISM

## The hazard rate and the reversed hazard rate orders, with applications to order statistics

### Asok K. Nanda^{1} and Moshe Shaked^{2}

^{1}Department of Mathematics, Indian Institute of
Technology, Kharagpur 721 302, India

^{2}Department 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.

**Source**
(TeX , DVI )