143
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Analysis of Order Statistics from Distributions with Regularly Varying Tails

, &
Pages 2702-2713 | Received 27 Aug 2011, Accepted 02 Apr 2012, Published online: 05 Jun 2014

References

  • Balakrishnan, N. (2007). Permanents, order statistics, outliers, and robustness. Revista Matemática Complutense 20:7107.
  • Barlow, R.E., Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. Silver Spring, MD: To Begin With.
  • Bingham, N.H., Goldie, C.M., Teugels, J. (1987). Regular Variation. Cambridge: Cambridge University Press.
  • Block, H., Li, Y., Savits, T.H. (2003). Initial and final behavior of failure rate functions for mixtures and systems. J. Appl. Probab. 40:721740.
  • David, H.A., Nagaraja, H.N. (2003). Order Statistics. 3rd ed. New York: Wiley.
  • Embrechts, P., Klüppelberg, C., Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. New York: Springer.
  • Kleiber, C. (2002). Variability ordering of heavy-tailed distributions with applications to order statistics. Statist. Probab. Lett. 58:381388.
  • Kleiber, C. (2004). Lorenz ordering of order statistics from log-logistic and related distributions. J. Statist. Plann. Infer. 120:2004.
  • Kochar, S., Xu, M. (2007). Some recent results on stochastic comparisons and dependence among order statistics in the case of PHR model. J. Iran. Statist. Soc. 6:125140.
  • Kochar, S., Xu, M. (2009). Comparisons of parallel systems according to the convex transform order. J. Appl. Probab. 46:342352.
  • Mao, T., Hu, T. (2010). Equivlalent characterizations on orderings of order statistics and sample ranges. Probab. Eng. Inform. Sci. 24:245262.
  • Navarro, J. (2007). Tail hazard rate ording properties of order statistics and coherent systems. Nav. Res. Logist. 54:820828.
  • Navarro, J., Hernandez, P.J. (2008). Mean residual life functions of finite mixtures, order statistics and coherent systems. Metrika 67:277298.
  • Nolan, J.P. (2011). Stable distributions-Models for heavy tailed data. Boston: Birkhauser. In progress, Ch. 1 online at academic2.american.edu/∼jpnolan.
  • Resnick, S.I. (2007). Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. New York: Springer.
  • Rojo, J. (1992). A pure-tail ordering based on the ratio of the quantile functions. Ann. Statist. 20:570579.
  • Rojo, J. (1993). On the preservation of some pure-tail orderings by reliability operations. Statist. Probab. Lett. 17:189198.
  • Shaked, M., Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.