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The dilation order, the dispersion order, and orderings of residual lives

✍ Scribed by F. Belzunce; Franco Pellerey; J.M. Ruiz; Moshe Shaked

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
670 KB
Volume
33
Category
Article
ISSN
0167-7152

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✦ Synopsis

One purpose of this paper is to study the relationship of the dilation order (~dil) to two other stochastic orders: the mean residual life order (~ X ~<icx Y (the first implication holds under the assumption that at least one of the two underlying random variables satisfies some aging property). Thus, we refine the result of Theorem 3.A.13 in Shaked and Shanthikumar (1994).
Another purpose of this paper is to identify conditions under which all the residual lives, that are associated with two random variables X and Y, are ordered according to the dilation or the dispersion orders. Some of these results extend parts (a) and (b) of Theorem 2.B.13 in Shaked and Shanthikumar (1994).

πŸ“œ SIMILAR VOLUMES

The Laplace order and ordering of residu
The Laplace order and ordering of residual lives
✍ FΓ©lix Belzunce; Eva Ortega; JosΓ© M. Ruiz πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 120 KB

The purpose of this paper is to study new notions of stochastic comparisons and aging classes based on the Laplace transform order of residual lives. We give relationships to other stochastic orders and aging classes given previously. Finally we study some applications to shock models.