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On the Increasing Convex Order of Relative Spacings of Order Statistics

Author

Listed:
  • Antonia Castaño-Martínez

    (Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11510 Puerto Real, Spain)

  • Gema Pigueiras

    (Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11510 Puerto Real, Spain)

  • Miguel A. Sordo

    (Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11510 Puerto Real, Spain)

Abstract

Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex order of relative spacings of two distributions from the case of consecutive spacings to general spacings. The sufficient conditions are given in terms of the expected proportional shortfall order. As an application, we compare relative deprivation within some parametric families of income distributions.

Suggested Citation

  • Antonia Castaño-Martínez & Gema Pigueiras & Miguel A. Sordo, 2021. "On the Increasing Convex Order of Relative Spacings of Order Statistics," Mathematics, MDPI, vol. 9(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:618-:d:517154
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    References listed on IDEAS

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    5. Satya R. Chakravarty & Conchita D'Ambrosio & Pietro Muliere, 2003. "Target Shortfall Orderings and Indices," Discussion Papers of DIW Berlin 340, DIW Berlin, German Institute for Economic Research.
    6. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2012. "Comparison of risks based on the expected proportional shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 292-302.
    7. Zhao, Peng & Zhang, Yiying, 2012. "On sample ranges in multiple-outlier models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 335-349.
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    9. Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    10. Félix Belzunce & Carolina Martínez-Riquelme, 2017. "On sufficient conditions for the comparison of some quantile-based measures," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6512-6527, July.
    11. Hu, Taizhong & Wei, Ying, 2001. "Stochastic comparisons of spacings from restricted families of distributions," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 91-99, May.
    12. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2013. "Comparison of concentration for several families of income distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1036-1045.
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    Cited by:

    1. Vasile Preda & Luigi-Ionut Catana, 2021. "Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders," Mathematics, MDPI, vol. 9(11), pages 1-22, May.

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