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STOCHASTIC ORDERINGS BETWEEN p-SPACINGS OF GENERALIZED ORDER STATISTICS FROM TWO SAMPLES

Published online by Cambridge University Press:  01 June 2006

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]; [email protected]
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]; [email protected]

Abstract

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to investigate conditions on the distributions and the parameters on which the generalized order statistics are based to establish the likelihood ratio ordering of general p-spacings and the hazard rate and the dispersive orderings of (normalizing) simple spacings from two samples. We thus strengthen and complement some results in Franco, Ruiz, and Ruiz [7] and Belzunce, Mercader, and Ruiz [5]. This article is a continuation of Hu and Zhuang [10].

Type
Research Article
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Bagai, I. & Kochar, S.C. (1986). On tail ordering and comparison of failure rates. Communications in Statistics: Theory and Methods 15: 13771388.Google Scholar
Balakrishnan, N., Cramer, E., & Kamps, U. (2001). Bounds for means and variances of progressive type II censored order statistics. Statistics & Probability Letters 54: 301315.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: 199224.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: 99120.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. 301372.
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: 471484.Google Scholar
Hu, T. & Zhuang, W. (2006). Stochastic comparisons of m-spacings. Journal of Statistical Planning and Inference 136: 3342.Google Scholar
Hu, T. & Zhuang, W. (2005). A note on stochastic comparisons of generalized order statistics. Statistics & Probability Letters 72: 163170.Google Scholar
Hu, T. & Zhuang, W. (2005). Stochastic properties of p-spacings of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 257276.Google Scholar
Kamps, U. (1995). A concept of generalized order statistics. Stuttgard: Teubner.
Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical Planning and Inference 48: 123.Google Scholar
Karlin, S. (1968). Total positivity. Stanford, CA: Stanford University Press.
Karlin, S. & Proschan, F. (1960). Pólya type distributions of convolutions. Annals of Mathematical Statistics 31: 721736.Google Scholar
Khaledi, B.-E. (2004). Some new results on stochastic orderings between generalized order statistics. Journal of Iranian Statistical Society (to appear).
Khaledi, B.-E. & Kochar, S. (1999). Stochastic orderings between distributions and their sample spacings—II. Statistics & Probability Letters 44: 161166.Google Scholar
Khaledi, B.-E. & Kochar, S. (2005). Dependence orderings for generalized order statistics. Statistics & Probability Letters 73: 357367.Google Scholar
Kochar, S.C. (1999). On stochastic orderings between distributions and their sample spacings. Statistics & Probability Letters 42: 345352.Google Scholar
Misra, N. & van der Meulen, E.C. (2003). On stochastic properties of m-spacings. Journal of Statistical Planning and Inference 115: 683697.Google Scholar
Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. West Sussex, UK: Wiley.
Sengupta, D. & Nanda, A.K. (1999). Log-concave and concave distributions in reliability. Naval Research Logistics 46: 419433.Google Scholar
Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. New York: Academic Press.
Xu, M. & Li, X. (2004). Likelihood ratio order and DFRA aging property of sample's m-spacings. Technical report, School of Mathematics and Statistics, Lanzhou University, Lanzhou, China.