Let X and Y be two random variables with finite expectations EX and EY, respectively. Then X is said to be smaller than Y in the dilation order if E[(phi(X - EX)] less than or equal to E[(phi(Y - EY)] for any convex function phi for which the expectations exist. In this paper we obtain a new characterization of the dilation order. This characterization enables us to give new interpretations to the dilation order, and using them we identify conditions which imply the dilation order. A sample of applications of the new characterization is given
Fagiuoli, E., Pellerey, F., Shaked, M. (1999). A characterization of the dilation order and its applications. STATISTICAL PAPERS, 40(4), 393-406 [10.1007/BF02934633].
A characterization of the dilation order and its applications
Fagiuoli, ERC;
1999
Abstract
Let X and Y be two random variables with finite expectations EX and EY, respectively. Then X is said to be smaller than Y in the dilation order if E[(phi(X - EX)] less than or equal to E[(phi(Y - EY)] for any convex function phi for which the expectations exist. In this paper we obtain a new characterization of the dilation order. This characterization enables us to give new interpretations to the dilation order, and using them we identify conditions which imply the dilation order. A sample of applications of the new characterization is given
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