Abstract
We consider finite random variables decomposed into the sum of two independent random variables, one of which belongs to the same type of distribution. We investigate the properties of characteristic functions based on the analysis of differential equations and allocate the class of distributions possessing some extreme properties of entropy.
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A. M. Kagan, Yu. V. Linnik, and S. R. Rao, Characterization Problems of Mathematical Statistics [in Russian], Nauka, Moscow (1972).
P. Levy, “ L’addition des variables aléatoires définies sur une circonférence,” Bull. Soc. Math. France, 67, No. 1, 2, 1–41 (1939).
Yu. V. Linnik, Decompositions of Probability Laws [in Russian], Izd. Leningr. Univer., Leningrad (1960).
V. L. Rvachev and V. O. Rvachev, “On one finite function,” DAN UkrRSR, Ser. A, 705–707 (1971).
E. Lukach, Characteristic Functions [in Russian], Nauka, Moscow (1979).
V. L. Rvachev and V. A. Rvachev, Nonclassical Methods of the Theory of Approximations in Boundary-Value Problems [in Russian], Naukova Dumka, Kyiv (1979).
S. R. Rao, Linear Statistical Methods and their Application [in Russian], Nauka, Moscow (1968).
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 100–106, May–June, 2015.
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Kabanov, K.I., Kolodyazhny, V.M. Characterization of the Distributions with Atomic Function Densities. Cybern Syst Anal 51, 410–415 (2015). https://doi.org/10.1007/s10559-015-9732-y
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DOI: https://doi.org/10.1007/s10559-015-9732-y