The Tukey and the random Tukey depths characterize discrete distributions

Authors:
J. A. Cuesta-Albertos;A. Nieto-Reyes
Affiliations:
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Spain;Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Spain
Venue:
Journal of Multivariate Analysis
Year:
2008

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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.