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Connections among various variability orderings

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  • Kochar, Subhash C.
  • Carrière, K. C.

Abstract

Recently, a new variability ordering, called right spread ordering or excess wealth ordering has been introduced. This new ordering is weaker than dispersive ordering. We show in this note that if X is less variable than Y in the sense of right spread ordering or convex ordering, then it implies that X1 - X2 is less variable than Y1 - Y2 according to increasing convex ordering. Here X1 and X2 (Y1 and Y2) are two independent copies of X (Y). An application of the right spread ordering in the study of spacings from an increasing mean residual life distribution is given.

Suggested Citation

  • Kochar, Subhash C. & Carrière, K. C., 1997. "Connections among various variability orderings," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 327-333, November.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:4:p:327-333
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    References listed on IDEAS

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    1. Kirmani, S. N. U. A., 1996. "On sample spacings from IMRL distributions," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 159-166, August.
    2. Muñoz-Perez, J., 1990. "Dispersive ordering by the spread function," Statistics & Probability Letters, Elsevier, vol. 10(5), pages 407-410, October.
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    Cited by:

    1. Xiaohu Li & Ming J. Zuo, 2004. "Preservation of stochastic orders for random minima and maxima, with applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 332-344, April.
    2. Bassan, Bruno & Denuit, Michel & Scarsini, Marco, 1999. "Variability orders and mean differences," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 121-130, November.
    3. Hu, Taizhong & Chen, Jing & Yao, Junchao, 2006. "Preservation of the location independent risk order under convolution," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 406-412, April.
    4. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
    5. Barmalzan, Ghobad & Payandeh Najafabadi, Amir T., 2015. "On the convex transform and right-spread orders of smallest claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 380-384.
    6. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    7. Belzunce, F. & Pinar, J. F. & Ruiz, J. M., 2001. "A family of tests for right spread order," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 79-92, August.
    8. Belzunce, F., 1999. "On a characterization of right spread order by the increasing convex order," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 103-110, November.
    9. Fernández-Ponce, J.M. & Pellerey, F. & Rodríguez-Griñolo, M.R., 2011. "A characterization of the multivariate excess wealth ordering," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 410-417.

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