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On Some Properties of the Multivariate Aging Classes

Published online by Cambridge University Press:  27 July 2009

S. P. Mukherjee  and
A. Chatterjee
S. P. Mukherjee
Affiliation:
Department of StatisticsUniversity of Calcutta, Calcutta-700 019, India
A. Chatterjee
Affiliation:
Department of StatisticsUniversity of Burdwan, Burdwan 713 104, West Bengal, India
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Abstract

Two multivariate aging classes described by Johnson and Kotz [7] and Zahedi [11] and known as vector multivariate increasing/decreasing hazard rate (VMIHR/VMDHR) class and decreasing/increasing multivariate mean remaining life of type 2 (DMMRL/IMMRL-2) class, respectively, as well as componentwise NBUE/NWUE class, are considered. The chain of implications between these classes and some characterizing properties of them with regard to the equilibrium distribution corresponding to a multivariate distribution function and concave (convex) transformation of the residual random vector have been established. The “closure under mixture’ property of the first two classes are also studied.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 4 , October 1991 , pp. 523 - 534
Copyright
Copyright © Cambridge University Press 1991

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