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The Tukey and the random Tukey depths characterize discrete distributions

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  • Cuesta-Albertos, J.A.
  • Nieto-Reyes, A.

Abstract

Through this paper it is shown that if the Tukey depths of two probabilities, P and Q, coincide and one of those distributions is discrete, then P=Q. The same is proved if the random Tukey depths coincide.

Suggested Citation

  • Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The Tukey and the random Tukey depths characterize discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2304-2311, November.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2304-2311
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    References listed on IDEAS

    as
    1. Cuesta-Albertos, J.A. & del Barrio, E. & Fraiman, R. & Matran, C., 2007. "The random projection method in goodness of fit for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4814-4831, June.
    2. Koshevoy, Gleb A., 2002. "The Tukey Depth Characterizes the Atomic Measure," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 360-364, November.
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    Cited by:

    1. Daniel Fraiman & Nicolas Fraiman & Ricardo Fraiman, 2017. "Nonparametric statistics of dynamic networks with distinguishable nodes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 546-573, September.
    2. Alicia Nieto-Reyes & Rafael Duque & Giacomo Francisci, 2021. "A Method to Automate the Prediction of Student Academic Performance from Early Stages of the Course," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    3. Stanislav Nagy, 2021. "Halfspace depth does not characterize probability distributions," Statistical Papers, Springer, vol. 62(3), pages 1135-1139, June.
    4. Laketa, Petra & Nagy, Stanislav, 2021. "Reconstruction of atomic measures from their halfspace depth," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

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