Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T04:40:24.109Z Has data issue: false hasContentIssue false
  • English
  • Français

ON STOCHASTIC AND AGING PROPERTIES OF GENERALIZED ORDER STATISTICS

Published online by Cambridge University Press:  31 March 2011

Mahdi Tavangar  and
Majid Asadi
Mahdi Tavangar
Affiliation:
Department of Statistics, University of Isfahan, Isfahan, 81744, Iran E-mails: m.tavangar@stat.ui.ac.ir; m.asadi@stat.ui.ac.ir
Majid Asadi
Affiliation:
Department of Statistics, University of Isfahan, Isfahan, 81744, Iran E-mails: m.tavangar@stat.ui.ac.ir; m.asadi@stat.ui.ac.ir
Get access Rights & Permissions [Opens in a new window]

Abstract

The generalized order statistics (GOS) model is a unified model that contains the well-known ordered random data such as order statistics and record values. In the present article, we investigate some stochastic ordering results and aging properties of the conditional GOS. The results of the article subsume some of the existing results, which recently are obtained in the literature, on conditional GOS. In particular, our results hold for the model of progressively type II right censored order statistics without any restriction on the censoring scheme.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 2 , April 2011 , pp. 187 - 204
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Arnold, B.C., Balakrishnan, N. & Nagaraja, H.N. (1992). A first course in order statistics. New York: Wiley.Google Scholar
2.Arnold, B.C., Balakrishnan, N. & Nagaraja, H.N. (1998). Records. New York: Wiley.Google Scholar
3.Asadi, M. (2006). On the mean past lifetime of the components of a parallel system. Journal of Statistical Planning and Inference 136: 1197–1206.Google Scholar
4.Asadi, M. & Bayramoglu, I. (2005). A note on the mean residual life function of a parallel system. Communications in statistics: Theory and Methods 34: 475–484.CrossRefGoogle Scholar
5.Asadi, M. & Bayramoglu, I. (2006). On the mean residual life function of the k-out-of-n systems at the system level. IEEE Transactions on Reliability 55: 314–318.Google Scholar
6.Asadi, M. & Raqab, M.Z. (2010). The mean residual of record values at the level of previous records. Metrika 72: 251–264.Google Scholar
7.Balakrishnan, N. & Aggarwala, R. (2000). Progressive censoring: Theory, methods and applications. Boston: Birkhauser.Google Scholar
8.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart, Winston.Google Scholar
9.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
10.Cha, J.H. & Mi, J. (2007). Some probability functions in reliability and their applications. Naval Research Logistics 54: 128–135.CrossRefGoogle Scholar
11.Cramer, E. & Kamps, U. (2001). Estimation with sequential order statistics from exponential distributions. Annals of the Institute of Statistical Mathematics 53: 307–324.Google Scholar
12.Cramer, E. & Kamps, U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika 58: 293–310.CrossRefGoogle Scholar
13.David, H.A. & Nagaraja, H.N. (2003). Order statistics. 3rd ed.Hoboken, NJ: Wiley.Google Scholar
14.Franco, M., Ruiz, J.M. & Ruiz, M.C. (2001). Stochastic orderings between spacings of generalized order statistics. Probability in the Engineering and Informational Sciences 16: 471–484.CrossRefGoogle Scholar
15.Hashemi, M., Tavangar, M. & Asadi, M. (2010). Some properties of the residual lifetime of progressively type II right censored order statistics. Statistics and Probability Letters 80: 845–859.Google Scholar
16.Hu, T., Jin, W. & Khaledi, B.-E. (2007). Ordering conditinoal ditributions of generalized order statistics. Probability in the Engineering and Informational Sciences 21: 401–417.Google Scholar
17.Hu, T. & Zhuang, W. (2005). A note on comparisons of generalized order statistics. Statistics and Probability Letters 72: 163–170.Google Scholar
18.Kamps, U. (1995). A concept of generalized order statistics. Stuttgart: Teubner.CrossRefGoogle Scholar
19.Karlin, S. (1968). Total positivity. Palo Alto, CA: Stanford University Press.Google Scholar
20.Khaledi, B.-E. & Shaked, M. (2007). Ordering conditional lifetimes of coherent systems. Journal of Statistical Planning and Inference 137: 1173–1184.Google Scholar
21.Khaledi, B.-E. & Shojaei, R. (2007). On stochastic ordering between residual record values. Statistics and Probability Letters 77: 1467–1472.Google Scholar
22.Li, X. & Zhao, P. (2006). Some aging properties of the residual life of k-out-of-n systems. IEEE Transaction on Reliability 55(3): 535–541.Google Scholar
23.Li, X. & Zhao, P. (2008). Stochastic comparison on general inactivity time and general residual life of k-out-of-n systems. Communications in Statistics: Simulation and Computation 37: 1005–1019.Google Scholar
24.Misra, N. & van der Meulen, E.C. (2003). On stochastic properties of m-spacings. Journal of Statistical Planning and Inference 115: 683–697.CrossRefGoogle Scholar
25.Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. New York: Wiley.Google Scholar
26.Raqab, M.Z. & Asadi, M. (2008). On the mean residual life of records. Journal of Statistical Planning and Inference 138: 3660–3666.Google Scholar
27.Raqab, M.Z. & Asadi, M. (2010). Some results on the mean residual waiting time of records. Statistics 44(5): 493–504.CrossRefGoogle Scholar
28.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.Google Scholar
29.Tavangar, M. & Asadi, M. (2011). Some results on conditional expectations of lower record values. Statistics. doi:10.1080/02331880903348481.CrossRefGoogle Scholar
30.Tavangar, M. & Asadi, M. (2010). A study on the mean past lifetime of the components of (n−k+1)-out-of-n system at the system level. Metrika 72: 59–73.Google Scholar
31.Tavangar, M. & Asadi, M. (2011). Some unified characterization results on the generalized Pareto distributions based on generalized order statistics. Metrika. Technical report.Google Scholar
32.Xie, H. & Hu, T. (2008). Conditional ordering of generalized order statistics revisited. Probability in the Engineering and Informational Sciences 22: 334–346.Google Scholar
33.Zardasht, V. & Asadi, M. (2010). Evaluation of P(X t>Y t) when both X t and Y t are residual lifetimes of two systems. Statistica Neerlandica 64(4): 460–481.Google Scholar
34.Zhao, P. & Balakrishnan, N. (2009). Stochastic comparisons and properties of conditional generalized order statistics. Journal of Statistical Planning and Inference 139: 2920–2932.Google Scholar