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ORDERING p-SPACINGS OF GENERALIZED ORDER STATISTICS REVISITED

Published online by Cambridge University Press:  13 November 2008

Hongmei Xie  and
Taizhong Hu
Hongmei Xie
Affiliation:
Department of Mathematics, Shihezi University, Shihezi, Xinjiang 832003, People's Republic of China
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: thu@ustc.edu.cn
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Abstract

In this article we investigate less restrictive conditions on the model parameters and the underlying distribution function upon which the generalized order statistics are based, which enable one to establish the likelihood ratio and the hazard ratio orderings for p-spacings of generalized order statistic. Some previous works in the literature are extended.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 1 , January 2009 , pp. 1 - 16
Copyright
Copyright © Cambridge University Press 2009

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References

1.Balakrishnan, N. (2007). Progressive censoring methodology: An appraisal. Test 16: 211–259.CrossRefGoogle Scholar
2.Balakrishnan, N. & Aggarwala, R. (2000). Progressive censoring: Theory, methods, and applications. Boston: Birkhäuser.CrossRefGoogle Scholar
3.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart & Winston.Google Scholar
4.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.CrossRefGoogle Scholar
5.Cramer, E. & Kamps, U. (2001). Sequential k-out-of-n systems. In: Balakrishnan, N. & Rao, C.R., (eds.) Handbook of statistics: Advances in reliability, Volume 20. Amsterdam: Elsevier, pp. 301–372.Google Scholar
6.Cramer, E. & Kamps, U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika 58: 293–310.CrossRefGoogle Scholar
7.Fang, Z., Hu, T., Wu, Y. & Zhuang, W. (2006). Multivariate stochastic orderings of spacings of generalized order statistics. Chinese Journal of Applied Probability and Statistics 22: 295–303.Google Scholar
8.Hu, T. & Zhuang, W. (2005). A note on stochastic comparisons of generalized order statistics. Statistics & Probability Letters 72: 163–170.CrossRefGoogle Scholar
9.Hu, T. & Zhuang, W. (2005). Stochastic properties of p-spacings of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 257–276.CrossRefGoogle Scholar
10.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.CrossRefGoogle Scholar
11.Kamps, U. (1995). A concept of generalized order statistics. Stuttgard: Teubner.CrossRefGoogle Scholar
12.Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical Planning and Inference 48: 1–23.CrossRefGoogle Scholar
13.Kamps, U. & Cramer, E. (2001). On distribution of generalized order statistics. Statistics 35: 268–280.CrossRefGoogle Scholar
14.Misra, N. & van der Meulen, E.C. (2003). On stochastic properties of m-spacings. Journal of Statistical Planning and Inference 115: 683–697.Google Scholar
15.Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. West Sussex, UK: Wiley.Google Scholar
16.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.Google Scholar
17.Xie, H. & Hu, T. (2008). Conditional ordering of generalized order statistics revisited. Probability in the Engineering and Informational Sciences 22: 333–346.CrossRefGoogle Scholar