On Lin’s Condition for Products of Random Variables with Singular Joint Distribution

• Autorzy: ll'inskii Alexander , Ostrovska Sofiya

Identyfikatory

DOI

10.37190/0208-4147.40.1.6

• Języki publikacji: EN

Abstrakty

EN

Lin’s condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin’s condition for functions of random variables have appeared. In the present paper, this condition is studied for products of random variables with given densities in the case when their joint distribution is singular. It is proved, assuming that the densities of both random variables satisfy Lin’s condition, that the density of their product may or may not satisfy this condition.

Słowa kluczowe

EN

random variable; singular distribution; Lin’s condition

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 1
• Strony: 97--104
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

ll'inskii Alexander

• Department of Mathematics and Informatics, Karazin National University, Kharkov, Ukraine

autor

Ostrovska Sofiya

• Department of Mathematics, Atilim University, 06830 Incek, Ankara, Turkey

Bibliografia

• [1] A. Il’inskii and S. Ostrovska, On Lin’s condition for products of random variables, Zh. Mat. Fiz. Anal. Geom. 15 (2019), 79-85.
• [2] P. Kopanov and J. Stoyanov, Lin’s condition for functions of random variables and moment determinacy of probability distributions, C. R. Acad. Bulgare Sci. 70 (2017), 611-618.
• [3] G. D. Lin, On the moment problems, Statist. Probab. Lett. 35 (1997), 85-90.
• [4] G. D. Lin, Recent developments on the moment problem, J. Statist. Distributions Appl. 4 (2017), 1-17.
• [5] G. D. Lin and J. Stoyanov, Moment determinacy of powers and products of nonnegative random variables. J. Theoret. Probab. 28 (2015), 1337-1353.
• [6] G. D. Lin and J. Stoyanov, On the moment determinacy of products of non-identically distributed random variables. Probab. Math. Statist. 36 (2016), 21-33.
• [7] A.G. Pakes, Remarks on converse Carleman and Krein criteria for the classical moment problem, J. Austral. Math. Soc. 71 (2001), 81-104.
• [8] D. Stirzaker, The Cambridge Dictionary of Probability and its Applications, Cambridge Univ. Press, 2015.
• [9] J. Stoyanov, Counterexamples in Probability, 3rd ed., Dover Publ., New York, 2013.
• [10] J. Stoyanov, Krein condition in probabilistic moment problems, Bernoulli 6 (2000), 939-949.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).