Abstract
In the study of probabilistic orders iterated integrals of survival functions have been used by many authors. Recently, dispersion-typestochastic orders have been defined by Belzunce, Hu and Khaledi (2003) [Probability in the Engineering and Informational Sciences, Vol. 17, pp. 305–334]. The purpose of this paper is to generalize the dispersion-type stochastic orders using generalized iterated survival functions. The relationships between generalized stochastic orders and the stochastic orders of dispersion-type have been studied. It is shown that under certain condition, generalized down stochastic orders imply generalized stochastic orders of dispersion-type which, in turn, imply generalized stochastic orders. Generalized stochastic orders of dispersion-type of residual random variables are discussed. Some characterizations of generalized stochastic orders of dispersion-type have also been studied. Some results regarding generalized orders are also discussed when the residual time is random.
AMS (2000) Subject Classification : 60E15, 60K10.
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