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COMMENTS ON “ORDERING PROPERTIES OF ORDER STATISTICS FROM HETEROGENEOUS POPULATIONS: A REVIEW WITH AN EMPHASIS ON SOME RECENT DEVELOPMENTS”

Published online by Cambridge University Press:  13 August 2013

Maochao Xu
Maochao Xu*
Affiliation:
Department of Mathematics, Illinois State University, Normal, IL, USA E-mail: [email protected]
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Abstract

Professors Balakrishnan and Zhao have written an excellent survey on the recent developments of stochastic comparisons of order statistics, which cover almost every aspect of ordering properties of order statistics from both continuous and discrete heterogeneous populations. My discussion will be limited to the skewness of order statistics and order statistics from heterogeneous populations with different shape parameters.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 4 , October 2013 , pp. 451 - 454
Copyright
Copyright © Cambridge University Press 2013 

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References

1.Barlow, R.E., Bartholomew, D.J., Bremner, J.M. & Brunk, H.D. (1972). Statistical inference under order restrictions. New York: John Wiley.Google Scholar
2.Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. MD: Silver Spring, To Begin With.Google Scholar
3.Bingham, N.H., Goldie, C.M. & Teugels, J. (1987). Regular variation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
4.Huang, Y., Li, Y. & Xu, M. (2013). Analysis of order statistics from distributions with regularly varying tails. Communications in Statistics-Theory and Methods, to appear.Google Scholar
5.Kochar, S. & Xu, M. (2009). Comparisons of parallel systems according to the convex transform order. Journal of Applied Probability, 46: 342–352.CrossRefGoogle Scholar
6.Kochar, S. & Xu, M. (2012). Some unified results on comparing linear combinations of independent gamma random variables. Probability in Engineering and Information Sciences, 49: 393–404.CrossRefGoogle Scholar
7.Kochar, S. & Xu, M. (2013). On the skewness of order statistics with applications. Annals of Operations Research, DOI: 10.1007/s10479-012-1212-4.Google Scholar
8.Marshall, A.W. & Olkin, I. (2007). Life distributions. New York: Springer.Google Scholar