López-Blázquez, Fernando; Miño, Begoña Salamanca A characterization of the geometric distribution. (English) Zbl 0888.62010 Stat. Pap. 39, No. 2, 231-236 (1998). 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. Cited in 4 Documents MSC: 62E10 Characterization and structure theory of statistical distributions 62J05 Linear regression; mixed models Keywords:geometric distribution; order statistics PDFBibTeX XMLCite \textit{F. López-Blázquez} and \textit{B. S. Miño}, Stat. Pap. 39, No. 2, 231--236 (1998; Zbl 0888.62010) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.