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On characterization of multivariate stable distributions via random linear statistics

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Abstract

LetX 1,X 2, ...,X n be independent and identically distributed random vectors inR d, and letY=(Y 1,Y 2, ...,Y n )′ be a random coefficient vector inR n, independent ofX /′j . We characterize the multivariate stable distributions by considering the independence of the random linear statistic

$$U = Y_1 X_1 + Y_2 X_2 + \cdot \cdot \cdot + Y_n X_n $$

and the random coefficient vectorY.

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Authors and Affiliations

  1. Department of Mathematics, University of Louisville, 40292, Louisville, Kentucky

    Wei-Bin Zeng

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  1. Wei-Bin Zeng
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Zeng, WB. On characterization of multivariate stable distributions via random linear statistics. J Theor Probab 8, 1–15 (1995). https://doi.org/10.1007/BF02213449

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  • DOI: https://doi.org/10.1007/BF02213449

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