Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-15T06:03:07.799Z Has data issue: false hasContentIssue false
  • English
  • Français

STOCHASTIC ORDERING OF A CLASS OF SYMMETRIC DISTRIBUTIONS

Published online by Cambridge University Press:  14 July 2009

Weiwei Zhuang  and
Taizhong Hu
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: weizh@ustc.edu.cn; thu@ustc.edu.cn
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: weizh@ustc.edu.cn; thu@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we investigate the sufficient and/or necessary conditions in order to stochastically compare the order statistics and their spacing vectors of two random vectors X and Y with special symmetric distributions. The conditions are imposed on the sample ranges Xn:n–X1:n and Yn:n–Y1:n or on (X1:n, Xn:n–X1:n) and (Y1:n, Yn:n–Y1:n). In particular, we consider the multivariate usual stochastic order, the convex order, the increasing convex order, and the directionally convex order. Several examples are also given to illustrate the power of the main results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 4 , October 2009 , pp. 583 - 595
Copyright
Copyright © Cambridge University Press 2009

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.Chi, Y., Yang, J., & Qi, Y. (2008). Decomposition of Schur-constant model and its applications. Insurance: Mathematics and Economics 44: 398–408.Google Scholar
2.Gnedin, A.V. (1994). A solution to the game of Googol. Annals of Probability 22: 1588–1595.CrossRefGoogle Scholar
3.Gnedin, A.V. (1996). On a class of exchangeable sequences. Statistics and Probability Letters 28: 159–164 [see also 25: 351–355].CrossRefGoogle Scholar
4.Iglesias, P., Pereira, C.B., & Tanaka, N.I. (1998). Characterizations of multivariate spherical distributions in the ℓ∞-norm. Test 7: 307–324.CrossRefGoogle Scholar
5.Kaas, R., Goovaerts, M.J., Dhaene, J., & Denuit, M. (2001). Modern actuarial risk theory. Dordrecht: Kluwer Academic.Google Scholar
6.Meester, L.E. & Shanthikumar, J.G. (1993). Regularity of stochastic processes: A theory of directional convexity. Probability in the Engineering and Informational Sciences 7: 343–360.CrossRefGoogle Scholar
7.Müller, A. (2001). Stochastic ordering of multivariate normal distributions. Annals of the Institute of Statistical Mathematics 53: 567–575.CrossRefGoogle Scholar
8.Müller, A. & Scarsini, M. (2001). Stochastic comparison of random vectors with a common copula. Mathematics of Operations Research 26: 723–740.CrossRefGoogle Scholar
9.Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks, West Sussex, UK: Wiley.Google Scholar
10.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
11.Shaked, M., Spizzichino, F., & Suter, F. (2002). Nonhomogeneous birth processes and ℓ∞-sperical densities, with applications in reliability theory. Probability in the Engineering and Informational Sciences 16: 271–288.CrossRefGoogle Scholar
12.Shaked, M., Spizzichino, F., & Suter, F. (2004). Uniform order statistics property and ℓ∞-sperical densities. Probability in the Engineering and Informational Sciences 18: 275–297 [Erratum: 22 (2008), 161–162].CrossRefGoogle Scholar
13.Yao, J. & Hu, T. (2008). Dependence structure of a class of symmetric distributions. Communications in Statistics: Theory and Methods 37: 1338–1346.CrossRefGoogle Scholar