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On a characteristic property of the uniform distribution

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Summary

LetX1,n≦X2,n≦...≦X n,n be the order statistics based on a sample from an absolutely continuous distributionF. It is proved that the uniform distribution on the interval [0,a] is characterized by the property thatX2,n−X1,n andX1,n are identically distributed.

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Authors and Affiliations

  1. The Institute of Statistical Mathematics, University of Guelph, Guelph, Canada

    R. Shimizu & J. S. Huang

Authors
  1. R. Shimizu
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  2. J. S. Huang
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Shimizu, R., Huang, J.S. On a characteristic property of the uniform distribution. Ann Inst Stat Math 35, 91–94 (1983). https://doi.org/10.1007/BF02480966

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  • DOI: https://doi.org/10.1007/BF02480966

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