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New properties and characterizations of the dispersive ordering

Author

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  • Rojo, Javier
  • He, Guo Zhong

Abstract

New characterizations of the dispersive ordering are established. These include a characterization in terms of the stochastic ordering of the sample spacings, preservation of the ordering by monotone convex (concave) transformations, and preservation of the ordering by truncation at the same quantile. The question of when the sample spacings inherit the dispersive ordering is investigated and, for the important special case of F or G being the exponential distribution, it is shown that F and G are ordered in dispersion if and only if the sample spacings also have the same order.

Suggested Citation

  • Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:4:p:365-372
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    Citations

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    Cited by:

    1. Rolf Aaberge & Steinar Bjerve & Kjell Doksum, 2005. "Modeling Concentration and Dispersion in Multiple Regression," Discussion Papers 412, Statistics Norway, Research Department.
    2. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    3. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
    4. Ebrahimi, Nader & Kirmani, S. N. U. A., 1996. "Some results on ordering of survival functions through uncertainty," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 167-176, August.
    5. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
    6. Carlos Carleos & Miguel López-Díaz, 2010. "A new family of dispersive orderings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 203-217, March.
    7. Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.
    8. Fernández-Ponce, J.M. & Rodríguez-Griñolo, R., 2006. "Preserving multivariate dispersion: An application to the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1208-1220, May.
    9. Longxiang Fang & N. Balakrishnan, 2016. "Likelihood ratio order of parallel systems with heterogeneous Weibull components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 693-703, August.
    10. Ayala, Guillermo & López-Díaz, Miguel, 2009. "The simplex dispersion ordering and its application to the evaluation of human corneal endothelia," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1447-1464, August.
    11. López-Díaz, Miguel, 2010. "Some remarks on Lp dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 413-420, March.
    12. Rolf Aaberge & Steinar Bjerve & Kjell Doksum, 2006. "Modeling inequality and spread in multiple regression," Papers math/0610852, arXiv.org.
    13. López-Díaz, Miguel, 2006. "An indexed multivariate dispersion ordering based on the Hausdorff distance," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1623-1637, August.
    14. Fang, Longxiang & Zhang, Xinsheng, 2013. "Stochastic comparisons of series systems with heterogeneous Weibull components," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1649-1653.
    15. Lisa Parveen & Ruhul Ali Khan & Murari Mitra, 2024. "A two sample nonparametric test for variability via empirical likelihood methods," Statistical Papers, Springer, vol. 65(7), pages 4243-4265, September.

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