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A characterization of the geometric distribution

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Abstract

We show that for a simple random sample from a discrete distribution on the positive integers, the regression ofX (2∶n) onX (1∶n) is linear with unit slope if and only if the distribution is geometric.

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References

  1. Arnold, B.C.;Balakrishnan, N. andNagaraja, H.N. (1992).A First Course in Order Statistics. Wiley, New York.

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  2. Ferguson, T.S. (1967). On Characterizing Distributions by Properties of Order Statistics.Sankhya A (29), 265–278.

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  3. Kirmani, S.N.U.A.; Alam, S.N. (1980). Characterization of the Geometric Distribution by the Form of a Predictor.Comm. Statist, 541–547.

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Authors and Affiliations

  1. Dpto. Estadística e I.O. Facultad de Matemáticas, Universidad de Sevilla, Tarfia, s/n, E-40012, Sevilla, Spain

    Fernando López-Blázquez & Begoña Salamanca Miño

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  1. Fernando López-Blázquez
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  2. Begoña Salamanca Miño
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Correspondence to Fernando López-Blázquez.

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López-Blázquez, F., Miño, B.S. A characterization of the geometric distribution. Statistical Papers 39, 231–236 (1998). https://doi.org/10.1007/BF02925410

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  • DOI: https://doi.org/10.1007/BF02925410

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