Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T22:43:41.976Z Has data issue: false hasContentIssue false
  • English
  • Français

TP2 DEPENDENCE OF SAMPLE SPACINGS WITH APPLICATIONS

Published online by Cambridge University Press:  19 March 2008

Xiaohu Li ,
Xiaoxiao Hu  and
Zhouping Li
Xiaohu Li
Affiliation:
School of Mathematics and Statistics, Lanzhou UniversityLanzhou 730000, China E-mail: [email protected]
Xiaoxiao Hu
Affiliation:
School of Mathematics and Statistics, Lanzhou UniversityLanzhou 730000, China E-mail: [email protected]
Zhouping Li
Affiliation:
School of Mathematics and Statistics, Lanzhou UniversityLanzhou 730000, China E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This article investigates TP2 dependence of sample spacings. It is proved that TP2 (RR2) dependence between a general spacing and a nonadjacent order statistic might be characterized by the DLR (ILR) property of the parent distribution, and TP2 dependence between any pair of consecutive spacings might be characterized by the DLR aging property of the population. Furthermore, TP2 dependence between any two consecutive spacings in multiple outliers exponential models is also derived. In addition, some applications in reliability and business auction are presented as well.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 2 , March 2008 , pp. 287 - 300
Copyright
Copyright © Cambridge University Press 2008

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.Bapat, R.B. & Beg, M.I. (1989). Order statistics for non-identically distributed variables and permanents. Sankhyá Series A 51: 78–93.Google Scholar
2.Bapat, R.B. & Kochar, S.C. (1994). On likelihood-ratio ordering of order statistics. Linear Algebra and its Applications 199: 281–291.CrossRefGoogle Scholar
3.Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To Begin with.Google Scholar
4.Belzunce, F., Franco, M., & Ruiz, J.M. (1999). On aging properties based on the residual life of k-out-of-n systems. Probability in the Engineering and Informational Sciences 13: 193–199.CrossRefGoogle Scholar
5.Bulow, P. & Klemperer, P. (1996). Auctions versus negotiations. American Economic Review 86: 180–194.Google Scholar
6.Hu, T., Wang, T., & Zhu, Z. (2006). Stochastic comparisons and dependence of spacings from two samples of exponential random variables. Communications in Statistics: Theory and Methods 35: 979–988.CrossRefGoogle Scholar
7.Hu, T. & Zhuang, W. (2006). Stochastic comparisons of m-spacings. Journal of Statistics Planning and Inference 136: 33–42.CrossRefGoogle Scholar
8.Karlin, S. (1968). Total positivity. Vol. I. Stanford, CA: Standford University Press.Google Scholar
9.Karlin, S. & Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities I. Multivariate totally positive distributions. Journal of Multivariate Analysis 10: 467–498.CrossRefGoogle Scholar
10.Karlin, S. & Rinott, Y. (1980). Classes of orderings of measures and related correlation inequalities I. Multivariate totally positive distributions. Journal of Multivariate Analysis 10: 499–516.CrossRefGoogle Scholar
11.Khaledi, B.E. & Kochar, S. (2000). Dependence among spacings. Probability in the Engineering and Informational Sciences 14: 461–472.CrossRefGoogle Scholar
12.Khaledi, B.E. & Kochar, S.C. (2001). Dependence properties of multivariate mixture distributions and their applications. Annals of the Institute of Statistical Mathematics 53: 620–630.CrossRefGoogle Scholar
13.Kim, S.H. & David, H.A. (1990). On the dependence structure of order statistics and concomitants of order statistics. Journal of Statistical Planning and Inference 24: 363–368.CrossRefGoogle Scholar
14.Kochar, S.C. (1998). Stochastic comparisons of spacings and order statistic. In Basu, A.P., Basu, S.K., & Mukhopadhyay, S. (eds.), Frontier in reliability. Singapore: World Scientific, pp. 201–216.CrossRefGoogle Scholar
15.Kochar, S.C. (1999). On stochastic orderings between distributions and their sample spacings. Statistics and Probability Letters 42: 345–352.CrossRefGoogle Scholar
16.Langberg, N.A., Leon, R.V., & Prochan, F. (1980). Characterizations of non-parametric classes of life distributions. The Annals of Probability 8: 1163–1170.CrossRefGoogle Scholar
17.Li, X. (2005). A note on the expected rent in auction theory. Operations Research Letters 33: 531–534.CrossRefGoogle Scholar
18.Li, X. & Chen, J. (2004). Aging properties of the residual life length of k-out-of-n systems with independent but non-identical components. Applied Stochastic Models in Business and Industry 20: 143–153.CrossRefGoogle Scholar
19.Li, X. & Zuo, M. (2002). On the behaviour of some new aging properties based upon the residual life of k-out-of-n. Journal of Applied Probability 39: 426–433.CrossRefGoogle Scholar
20.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
21.Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. New York: Wiley.Google Scholar
22.Paul, A. & Gutierrez, G. (2004). Mean sample spacings, sample size and variability in auction-theoretic framework. Operations Research Letters 32: 103–108.CrossRefGoogle Scholar
23.Wen, S., Lu, Q., & Hu, T. (2007). Likelihood ratio orderings of spacings of heterogeneous exponential random variables. Journal of Multivariate Analysis 98: 743–756.CrossRefGoogle Scholar
24.Xu, M. & Li, X. (2006). Likelihood ratio order of m-spacings for two samples. Journal of Statistical Planning and Inference 136: 4250–4258.CrossRefGoogle Scholar