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MULTIVARIATE STOCHASTIC COMPARISONS OF SEQUENTIAL ORDER STATISTICS

Published online by Cambridge University Press:  15 December 2006

Weiwei Zhuang  and
Taizhong Hu
Weiwei Zhuang
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, E-mail: [email protected]
Taizhong Hu
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, E-mail: [email protected]
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Abstract

In this article we investigate conditions on the underlying distribution functions on which the sequential order statistics are based, to obtain stochastic comparisons of sequential order statistics in the multivariate likelihood ratio, the multivariate hazard rate, and the usual multivariate stochastic orders. Some applications of the main results are also given.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 1 , January 2007 , pp. 47 - 66
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Balakrishnan, N. & Aggarwala, R. (2000). Progressive censoring. Boston: Birkhauser.CrossRef
Balakrishnan, N., Cramer, E., & Kamps, U. (2001). Bounds for means and variances of progressive type II censored order statistics. Statistics and Probability Letters 54: 301–315.Google Scholar
Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To begin with.
Belzunce, F., Lillo, R.E., Ruiz, J.M., & Shaked, M. (2001). Stochastic comparisons of nonhomogeneous processes. Probability in the Engineering and Informational Sciences 15: 199–224.Google Scholar
Belzunce, F., Mercader, J.A., & Ruiz, J.M. (2003). Multivariate aging properties of epoch times of nonhomogeneous processes. Journal of Multivariate Analysis 84: 335–350.Google Scholar
Belzunce, F., Mercader, J.A., & Ruiz, J.M. (2005). Stochastic comparisons of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 99–120.Google Scholar
Cramer, E. & Kamps, U. (2001). Sequential k-out-of-n systems. In: N. Balakrishnan & C.R. Rao (eds.), Handbook of statistics: Advances in reliability, Vol. 20, Amsterdam: Elsevier, pp. 301–372.
Cramer, E. & Kamps, U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika 58: 293–310.Google Scholar
Franco, M., Ruiz, J.M., & Ruiz, M.C. (2002). Stochastic orderings between spacings of generalized order statistics. Probability in the Engineering and Informational Sciences 16: 471–484.Google Scholar
Hu, T. & Zhuang, W. (2005). A note on stochastic comparisons of generalized order statistics. Statistics and Probability Letters 72: 163–170.Google Scholar
Hu, T. & Zhuang, W. (2005). Stochastic properties of p-spacings of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 257–276.Google Scholar
Hu, T. & Zhuang, W. (2006). Stochastic orderings between p-spacings of generalized order statistics from two samples. Probability in the Engineering and Informational Sciences 20: 465–479.Google Scholar
Kamps, U. (1995). A concept of generalized order statistics. Stuttgard: Teubner.CrossRef
Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical Planning and Inference 48: 1–23.Google Scholar
Khaledi, B.-E. (2005). Some new results on stochastic orderings between generalized order statistics. Journal of Iranian Statistical Society 4: 35–49.Google Scholar
Khaledi, B.-E. & Kochar, S.C. (2005). Dependence orderings for generalized order statistics. Statistics and Probability Letters 73: 357–367.Google Scholar
Korwar, R. (2003). On the likelihood ratio order for progressive type II censored order statistics. Sankhya 65: 793–798.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.