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A Discrete Analogue of Terrell’s Characterization of Rectangular Distributions

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Abstract

Terrell [18] showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular (uniform over some interval) distributions. In the present note it is proved that the same is true for the discrete case, in the sense that the correlation coefficient attains its maximal value only for discrete rectangular (uniform over some finite lattice) distributions.

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ACKNOWLEDGMENTS

The author would like to cordially thank an anonymous Referee for careful reading of the manuscript, and for the correction of some mistakes and typos. Thanks are also due to Fernando López-Blázquez, Universidad de Sevilla, for useful discussions.

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Authors and Affiliations

  1. National and Kapodistrian University of Athens, Department of Mathematics, Section of Statistics and Operations Research, Panepistemiopolis, 15784, Athens, Greece

    Nickos Papadatos

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  1. Nickos Papadatos
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Papadatos, N. A Discrete Analogue of Terrell’s Characterization of Rectangular Distributions. Math. Meth. Stat. 32, 122–132 (2023). https://doi.org/10.3103/S1066530723020035

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  • DOI: https://doi.org/10.3103/S1066530723020035

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