Geodesic
Recurrent formation of discrete probabilistic distributions of random sets of events
Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 47-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

The class of discrete probabilistic distributions of the II type of a random set on a set of $N$ events is investigated. For constructing such probabilistic distributions, a recurrent formula and associative functions are offered to use. The advantage of the approach is that for the definition of the probabilistic distribution, instead of $2^N$ probabilities of events, it is enough to know $N$ probabilities and the type of the associative function. This approach is tested for some three associative functions. The theorems establishing their forms and the legitimacy conditions for obtained probabilistic distributions of random sets of events are proven.
Keywords: random set of events, discrete probability distributions, associative function. 
@article{PDM_2014_4_a4,
     author = {D. V. Semenova and N. A. Lukyanova},
     title = {Recurrent formation of discrete probabilistic distributions of random sets of events},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {47--58},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_4_a4/}
}
TY  - JOUR
AU  - D. V. Semenova
AU  - N. A. Lukyanova
TI  - Recurrent formation of discrete probabilistic distributions of random sets of events
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 47
EP  - 58
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_4_a4/
LA  - ru
ID  - PDM_2014_4_a4
ER  - 
%0 Journal Article
%A D. V. Semenova
%A N. A. Lukyanova
%T Recurrent formation of discrete probabilistic distributions of random sets of events
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 47-58
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_4_a4/
%G ru
%F PDM_2014_4_a4
D. V. Semenova; N. A. Lukyanova. Recurrent formation of discrete probabilistic distributions of random sets of events. Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 47-58. http://geodesic.mathdoc.fr/item/PDM_2014_4_a4/

[1] Nguyen H. T., An Introduction to Random Sets, Taylor Francis Group, LLC, Boca Raton, 2006, 240 pp. | MR

[2] Shiryaev A. N., Veroyatnost-1, MTsNMO, M., 2004, 519 pp.

[3] Vorobev O. Yu., Vorobev A. O., “Summirovanie set-additivnykh funktsii i formula obrascheniya Mëbiusa”, Doklady RAN, 336:4 (2009), 417–420 | MR

[4] Semenova D. V., “On new notion of quasi-entropies of eventological distribution”, Proc. Second IASTED Intern. Multi-Conf. Automation Control and Inform. Technology, ACTA PRESS, Novosibirsk, 2005, 380–385

[5] Vorobyev O. Yu., Lukyanova N. A., “Properties of the entropy of multiplicative-truncated approximations of eventological distributions”, J. Siberian Federal University. Math. Physics, 4:1 (2011), 50–60

[6] Semenova D. V., Lukyanova N. A., “Random set decomposition of joint distribution of random variables of mixed type”, Proc. IAM, 1:2 (2012), 50–60

[7] Semenova D. V., Shangareeva L. Yu., “Associative Ali-Mikhail-Haq's random set”, Proc. scientific-applied conf. “Statistics and its Applications”, National University of Uzbekistan, Tashkent, 2013, 88–94

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

[9] Nelsen R. B., An Introduction to Copulas, second edition, Springer Science+Business Media, Inc., N.Y., 2006, 270 pp. | MR | Zbl

[10] Menger K., “Statistical metrics”, Proc. Nat. Acad. Sci. USA, 8 (1942), 535–537 | DOI | MR

[11] Schweizer B., Sklar A., Probabilistic Metric Spaces, North Holland, N.Y., 1983, 275 pp. | MR | Zbl

[12] Klement E. P., Mesiar R., Pap E., Triangular Norms, Kluwer Academic Pub., Boston, 2000, 220 pp. | MR | Zbl

[13] E. P. Klement, R. Mesiar (eds.), Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, Elsevier, Amsterdam, 2005, 481 pp. | MR

[14] Orlov A. I., Nechislovaya statistika, MZ-Press, M., 2004, 513 pp.

[15] Goldenok E. E., Lukyanova N. A., Semenova D. V., “Applications of wide dependence theory in eventological scoring”, Proc. IASTED Intern. Conf. Automation Control and Inform. Technology, Control, Diagnostics, and Automation, ACTA Press, Novosibirsk–Anaheim–Calgary–Zurich, 2010, 316–322