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

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  • Kleiber, Christian

Abstract

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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Bibliographic Info

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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Related research

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

References

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  1. Wilfling, Bernd, 1996. "Lorenz ordering of power-function order statistics," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 313-319, November.
  2. Kochar, Subhash C., 1996. "Dispersive ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 27(3), pages 271-274, April.
  3. Arnold, Barry C. & Villaseñor, Jose A., 1986. "Lorenz ordering of means and medians," Statistics & Probability Letters, Elsevier, vol. 4(1), pages 47-49, January.
  4. Arnold, Barry C. & Nagaraja, H. N., 1991. "Lorenz ordering of exponential order statistics," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 485-490, June.
  5. Lillo, Rosa E. & Nanda, Asok K. & Shaked, Moshe, 2001. "Preservation of some likelihood ratio stochastic orders by order statistics," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 111-119, January.
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Cited by:
  1. Christian Kleiber, 2007. "The Lorenz curve in economics and econometrics," Working papers 2007/09, Faculty of Business and Economics - University of Basel.
  2. Kochar, Subhash, 2006. "Lorenz ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1855-1860, November.
  3. 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, vol. 70(4), pages 759-772, December.

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