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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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References

Arnold, B.C. & Zahedi, H. (1988). On multivariate mean remaining life functions. Journal of Multivariate Analyis 25: 1–9.CrossRefGoogle Scholar
Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. Probability models. New York: Holt, Rinehart and Winston.Google Scholar
Block, H.W. (1977). Multivariate reliability classes. In Krishnaiah, P.R. (ed.), Applications of statistics. New York: North Holland, pp. 79–88.Google Scholar
Galambos, J. & Kotz, S. (1978). Characterizations of probability distribution. Lecture notes in mathematics, Vol. 675. Doldand, A. and Eckmans, B. (eds.). New York: Springer-Verlag.CrossRefGoogle Scholar
Haines, A.L. & Singpurwalla, N.D. (1975). Some contributions to the stochastic characterization of wear. In Proschan, F. & Serfling, R. (eds.), Reliability and biometry–Statistical analysis of life lengths. Philadelphia: Society of Industrial Application of Mathematics, pp. 47–80.Google Scholar
Hardy, G.H., Littlewood, J.E. & Polya, G. (1959). Inequalities. New York: Cambridge University Press.Google Scholar
Johnson, N.L. & Kotz, S. (1975). A vector multivariate hazard rate. Journal of Multivariate Analysis 5: 53–66.CrossRefGoogle Scholar
Johnson, N.L. & Kotz, S. (1975). Erratum, Journal of Multivariate Analysis: 498.Google Scholar
Loeve, M. (1960). Probability theory. New York: D. Van Nostrand Co.Google Scholar
Marshall, A.W. (1975). Multivariate distributions with monotone hazard rate. In Barlow, R.E., Fussel, J.B. & Singpurwalla, N.D. (eds.), Reliability and fault tree analysis. Philadelphia: SIAM.Google Scholar
Mukherjee, S.P. & Chatterjee, A. (1989). IFR closure property revisited. Unpublished manuscript.Google Scholar
Zahedi, H. (1985). Some new classes of multivariate survival functions. Journal of Statistical Planning and Inference 11: 171–188.CrossRefGoogle Scholar