Bertin, Emile M. J.; Theodorescu, Radu Some characterizations of discrete unimodality. (English) Zbl 0541.62006 Stat. Probab. Lett. 2, 23-30 (1984). This paper gives a characterization theorem and a representation theorem for lattice unimodal distribution functions. The results are in terms of Lévy concentration functions and they may be viewed as variants of the results arrived at earlier in the case of non-lattice distributions by the authors and W. Hengartner, Z. Wahrscheinlichkeitstheorie Verw. Geb. 57, 327-338 (1981; Zbl 0443.60015). Reviewer: D.N.Shanbhag Cited in 1 ReviewCited in 8 Documents MSC: 62E10 Characterization and structure theory of statistical distributions 60E05 Probability distributions: general theory 26A51 Convexity of real functions in one variable, generalizations Keywords:discrete unimodality; discrete distribution; mode; characterization; representation theorem; lattice unimodal distribution functions; Lévy concentration functions Citations:Zbl 0443.60015 PDFBibTeX XMLCite \textit{E. M. J. Bertin} and \textit{R. Theodorescu}, Stat. Probab. Lett. 2, 23--30 (1984; Zbl 0541.62006) Full Text: DOI Link References: [1] Bertin, E. M.J; Hengartner, W.; Theodorescu, R., Some characterizations of unimodal distribution functions, Z. Wahrsch. Verw. Gebiete, 57, 327-338 (1981) · Zbl 0443.60015 [2] Bertin, E. M.J; Theodorescu, R., Characterizations of unimodal distribution functions, (Dugué, D.; Lukacs, E.; Rohatgi, V. K., Analytical Methods in Probability Theory. Analytical Methods in Probability Theory, Lecture Notes in Mathematics, 861 (1981), Springer: Springer Berlin), 10-14, Oberwolfach 1980 · Zbl 0474.62015 [3] Hengartner, W.; Theodorescu, R., Concentration functions (1973), Academic Press: Academic Press New York, revised Russian version (1980): Nauka, Moscow · Zbl 0323.60015 [4] Hengartner, W.; Theodorescu, R., A characterization of strictly unimodal distribution functions by their concentration functions, Publ. Inst. Statist. Paris, 24, 1-10 (1978) [5] Keilson, J.; Gerber, H., Some results for discrete unimodality, J. Amer. Statist. Assoc., 66, 386-389 (1971) · Zbl 0236.60017 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.