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Variability ordering of heavy-tailed distributions with applications to order statistics


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  • Kleiber, Christian


Based on a necessary condition for variability ordering of distributions with regularly varying tails it is shown that, for such distributions, order statistics from the same sample are not comparable in the sense of several well-known variability orders. General restrictions in the two-sample case are also indicated.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 58 (2002)
Issue (Month): 4 (July)
Pages: 381-388

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Handle: RePEc:eee:stapro:v:58:y:2002:i:4:p:381-388

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Keywords: Dilation order Dispersive order Lorenz order Star-shaped order Convex (transform) order Order statistics Regular variation;


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  1. Wilfling, Bernd, 1996. "Lorenz ordering of power-function order statistics," Statistics & Probability Letters, Elsevier, Elsevier, vol. 30(4), pages 313-319, November.
  2. Lillo, Rosa E. & Nanda, Asok K. & Shaked, Moshe, 2001. "Preservation of some likelihood ratio stochastic orders by order statistics," Statistics & Probability Letters, Elsevier, Elsevier, vol. 51(2), pages 111-119, January.
  3. Kochar, Subhash C., 1996. "Dispersive ordering of order statistics," Statistics & Probability Letters, Elsevier, Elsevier, vol. 27(3), pages 271-274, April.
  4. Arnold, Barry C. & Nagaraja, H. N., 1991. "Lorenz ordering of exponential order statistics," Statistics & Probability Letters, Elsevier, Elsevier, vol. 11(6), pages 485-490, June.
  5. Arnold, Barry C. & Villaseñor, Jose A., 1986. "Lorenz ordering of means and medians," Statistics & Probability Letters, Elsevier, Elsevier, vol. 4(1), pages 47-49, January.
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Cited by:
  1. James Townsend & Hans Colonius, 2005. "Variability of the MAX and MIN Statistic: A Theory of the Quantile Spread as a Function of Sample Size," Psychometrika, Springer, Springer, vol. 70(4), pages 759-772, December.
  2. Kleiber, Christian, 2005. "The Lorenz curve in economics and econometrics," Technical Reports 2005,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  3. Kochar, Subhash, 2006. "Lorenz ordering of order statistics," Statistics & Probability Letters, Elsevier, Elsevier, vol. 76(17), pages 1855-1860, November.


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