For given real and monotone functionshi's, we obtain the necessary and sufficient conditions in order that any n-valuated function[Psi](x) be the conditional expectationE(h(X)/X>x) of a discrete random vectorX, whereh(X) denotes the random vector (h1(X1), ..., hn(Xn)).

One purpose of this paper is to study the relationship of the dilation order ([less-than-or-equals, slant]dil) to two other stochastic orders: the mean residual life order ([less-than-or-equals, slant]mrl) and the increasing convex order ([less-than-or-equals, slant]icx). Regarding these orders,...

The dispersive orderings arise in a great variety of contexts. In this paper we bridge the gap between dispersive orderings and ageing classes. We give characterizations of the IFR(DFR) and DMRL(IMRL) classes in terms of the dispersive and dilation orderings.

In this paper we address the problem of testing the equality in the right spread order of two random variables. We develop a family of tests statistics for right spread order. This technique is also used for testing NBUE [NWUE] aging classes. For these tests, we provide asymptotic results, and...

The limiting behavior of the hazard rate of coherent systems based on sequential order statistics is examined. Related results for the survival function of the system lifetime are also considered. For deriving the results, properties of limits involving a relevation transform are studied in...