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CONDITIONAL ORDERING OF GENERALIZED ORDER STATISTICS REVISITED

Published online by Cambridge University Press:  27 May 2008

Hongmei Xie
Affiliation:
Department of MathematicsShihezi UniversityShihezi, Xinjiang 832003, People's Republic of China
Taizhong Hu
Affiliation:
Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefei, Anhui 230026, People's Republic of China E-mail: [email protected]

Abstract

In this article we investigate less restrictive conditions on the model parameters that enable one to establish the likelihood ratio ordering of one generalized order statistic by conditioning on the right tail of another lower-indexed generalized order statistic. One application of the main results is also presented.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2008

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References

1Balakrishnan, N. (2007). Progressive censoring methodology: An appraisal. Test 16: 211259.CrossRefGoogle Scholar
2Balakrishnan, N. & Aggarwala, R. (2000). Progressive censoring: Theory, methods, and applications. Boston: Birkhäuser.Google Scholar
3Belzunce, F., Mercader, J.A. & Ruiz, J.M. (2005). Stochastic comparisons of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 99120.CrossRefGoogle Scholar
4Cramer, E. & Kamps, U. (2001). Sequential k-out-of-n systems. In: Balakrishnan, N. & Rao, C.R. (eds.), Handbook of statistics: Advances in reliability, Vol. 20. Amsterdam: Elsevier, pp. 301372.Google Scholar
5Cramer, E. & Kamps, U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika 58: 293310.Google Scholar
6Hu, T., Jin, W. & Khaledi, B.-E. (2007). Ordering conditional distributions of generalized order statistics. Probability in the Engineering and Informational Sciences 21: 401417.Google Scholar
7Hu, T., Li, X., Xu, M. & Zhuang, W. (2006). Some new results on ordering conditional distributions of generalized order statistics. Technical report, Department of Statistics and Finance, University of Science and Technology of China, Hefei.Google Scholar
8Hu, T. & Zhuang, W. (2005). A note on stochastic comparisons of generalized order statistics. Statistics and Probability Letters 72: 163170.Google Scholar
9Kamps, U. (1995). A concept of generalized order statistics. Stuttgard: Teubner.CrossRefGoogle Scholar
10Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical Planning and Inference 48: 123.Google Scholar
11Kamps, U. & Cramer, E. (2001). On distribution of generalized order statistics. Statistics 35: 268280.CrossRefGoogle Scholar
12Khaledi, B.-E. & Shaked, M. (2007). Ordering conditional lifetimes of coherent systems. Journal of Statistical Planning and Inference 137: 11731184.Google Scholar
13Khaledi, B.-E. & Shojaer, R. (2007). On stochastic orderings between residual record values. Statistics and Probability Letters 77: 14671472.Google Scholar
14Misra, N. & van der Meulen, E.C. (2003). On stochastic properties of m-spacings. Journal of Statistical Planning and Inference 115: 683697.Google Scholar
15Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. West Sussex, UK: Wiley.Google Scholar
16Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
17Zhuang, W. & Hu, T. (2007). Stochastic comparisons of sequential order statistics. Probability in the Engineering and Informational Sciences 21: 4766.CrossRefGoogle Scholar