Geodesic
Associative Frank functions in constructing families of discrete probability distributions of random sets of events
Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 5-19.

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Discrete probability distributions of random subsets on a finite set of events are considered. A one-parameter family of Frank associative functions is applied for generating them. The related properties and characteristics of functions in this family are described. The form and the creation and existence conditions of obtained distributions are also described.
Keywords: random set of events, discrete probability distribution, associative function of Frank. 
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N. A. Lukyanova; D. V. Semenova. Associative Frank functions in constructing families of discrete probability distributions of random sets of events. Prikladnaâ diskretnaâ matematika, no. 2 (2016), pp. 5-19. http://geodesic.mathdoc.fr/item/PDM_2016_2_a0/

[1] Nguyen H. T., An Introduction to Random Sets, Chapman and Hall/CRC, 2006, 240 pp. | MR | Zbl

[2] Molchanov I., The Theory of Random Sets, Springer, N.Y., 2011, 488 pp. | MR

[3] Semenova D. V., Lukyanova N. A., “Recurrent formation of discrete probabilistic distributions of random sets of events”, Prikladnaya Diskretnaya Matematika, 2014, no. 4, 47–58 (in Russian)

[4] Lukyanova N. A., Semenova D. V., “The study of discrete probabilistic distributions of random sets of events using associative function”, J. SFU, Mathematics and Physics, 7:4 (2014), 500–514

[5] Semenova D. V., Lukyanova N. A., “Formation of probabilistic distributions of RSE by associative functions”, ITMM 2014, CCIS, 487, Springer International Publishing Switzerland, 2014, 377–386 | Zbl

[6] Alsina S., Frank M., Schveizer B., Associative Functions: Triangular Norms and Copulas, World Scientific Publishing Co. Pte. Ltd., Singapore, 2006, 237 pp. | MR | Zbl

[7] Frank M. J., “On the simultaneous associativity of $F(x,y)$ and $x+y-F(x,y)$”, Aequationes Math., 19 (1979), 194–226 | DOI | MR | Zbl

[8] Vorob'ev O. Yu., Vorob'ev A. O., “Summation of set-additive functions and Möbius inversion formula”, Doklady Akademii Nauk, 336:4 (2009), 417–420 (in Russian) | MR

[9] Vorob'ev O. Yu., Set-summation, Nauka Publ., Novosibirsk, 1993 (in Russian) | MR

[10] Vorob'ev O. Yu., Eventology, SFU Publ., Krasnoyarsk, 2007 (in Russian)

[11] Vorob'ev O. Yu., Fomin A. Yu., Regression analysis of random events, KSU Publ., Krasnoyarsk, 2004 (in Russian)

[12] Lukyanova N. A., Semenova D. V., “The use of associative functions to estimate the target event probability”, Proc. konf. “Statistika i ee primenenie” (Tashkent, 16–17 October, 2015), NUUz Publ., Tashkent, 2015, 91–98 (in Russian)