Journal of Siberian Federal University. Mathematics & Physics / Set Functions and Probability Distributions of a Finite Random Sets

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2017 10 (3)
Authors
Lukyanova, Natalia A.; Semenova, Daria V.
Contact information
Lukyanova, Natalia A.: Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Krasnoyarsk State Medical University Partisan Zheleznyak, 1, Krasnoyarsk, 660022 Russia; ; Semenova, Daria V.: Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Krasnoyarsk State Medical University Partisan Zheleznyak, 1, Krasnoyarsk, 660022 Russia;
Keywords
finite random set; set function; probability distribution
Abstract

This paper is the investigation of the probability distributions of a finite random set in which the set of random events are considered as a support of the finite random set. These probability distributions can be defined by six equivalent ways (distributions of the I-st — VI-th type). Each of these types of the probability distributions is the set function defined on the corresponding system of events. In this paper the sufficient conditions are formulated and proved. When these conditions are satisfied, then the set function determines the probability distributions of the finite random set of the II-nd and the V-th type. The found conditions supplement the known necessary conditions for the existence of the probability distributions of a finite random set of the II-nd and the V-th type

Pages
362–371
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/33626