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A characterization of the geometric distribution. (English) Zbl 0888.62010

Summary: We show that for a simple random sample from a discrete distribution on the positive integers, the regression of \(X_{(2:n)}\) on \(X_{(1:n)}\) is linear with unit slope if and only if the distribution is geometric.

MSC:

62E10 Characterization and structure theory of statistical distributions
62J05 Linear regression; mixed models
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References:

[1] Arnold, B. C.; Balakrishnan, N.; Nagaraja, H. N., A First Course in Order Statistics (1992), New York: Wiley, New York · Zbl 0850.62008
[2] Ferguson, T. S., On Characterizing Distributions by Properties of Order Statistics, Sankhya A, 29, 265-278 (1967) · Zbl 0155.27302
[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. · Zbl 0454.62015
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