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Some characterizations of discrete unimodality. (English) Zbl 0541.62006

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

MSC:

62E10 Characterization and structure theory of statistical distributions
60E05 Probability distributions: general theory
26A51 Convexity of real functions in one variable, generalizations

Citations:

Zbl 0443.60015
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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
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