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Dynamic multivariate aging notions in relability theory. (English) Zbl 0732.62094
This paper uses multivariate extensions of likelihood ratio, hazard rate and stochastic orderings to suggest a variety of possible definitions for increasing failure rate (IFR) and Polya frequency of order 2 \((PF_ 2)\) for random vectors. Logical relationships amongst the definitions are considered. Single classes of multivariate IFR and \(PF_ 2\) distributions emerge, which are recommended on theoretical and practical grounds. The former class is included in that introduced by E. Arjas [Math. Oper. Res. 6, 551-562 (1981; Zbl 0501.60091)].
Reviewer: J.Preater (Keele)

MSC:
62N05 Reliability and life testing
62H05 Characterization and structure theory for multivariate probability distributions; copulas
90B25 Reliability, availability, maintenance, inspection in operations research
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