Articles
| Open Access |
https://doi.org/10.37547/
LIMIT THEOREM FOR A STATISTIC PROPOSED BY V. HEFDLING
Abdullaev Abdumukhtor Ganievich , Associate Professor at the non-state higher educational institution “University of Economics and Pedagogy” (Andijan). Mamurov Egamnazar Narbaevich , Associate Professor of the Department of “Higher and Applied Mathematics” at the Tashkent University of Economics.Abstract
The article first proves a limit theorem for a sequence of random variables called “U-statistics,” introduced by V. Hefdling. The proven limit theorem generalizes the result of V. Hefdling's theorem to the case where the number of samples is a random variable. In the theorem, it is not required that the observation results of the sample size are independent of the where ( ); however, as there must exist a sequence of numbers - with ( ) and a positive random variable such that, is required.
Keywords
Generalized statistics, sample size, normal distribution, independence, random variable, U-statistics, sequence of positive integer-valued random variables, distribution function, symmetry with respect to arguments.
References
Hoeffding W. The strong law of large numbers for U-statistics.—Inst. Of Stat. Univ. of N. Carolins, Mimeograph Series, N 302,1961.
Attila C. A theorem on departure of randomly indexed U – statistics from normality with an application in fixed-width sequential interval estimation.—Sankhya: The Indian J. Stat. v.43 1981, ser.A,1, p. 84-89.
Sproule R. Asymptotic properties of U- statistics.—Trans. Amer. Math. Soc.,v199,1974,p.55-64.
Robbins H. The asymptotic distribution of the sum of a random number of random variables. -- Bull. Amer. Math. Soc.,54,1948,p.1151-1161.
Mogyorodi J. A central limit theorem for the sum of random number of independent random variables.- Publ. Math. Inst. Hung. Acad. Sci., v.7, 1962,p. 409-424.
. Blum J.R., Hanson D. L. and Rosenblatt J.I. On the central limit theorem for the sum of a random number of independent random variables.- Zeit. Wahr. Vew Gebiet. 1, 1963, p. 389-393.
Jamirzaev A.A. Generalizations of A.Ya. Khinchin's Theorem on Relative Stability. - Scientific Papers of Tashkent State University, vol. 402, 1972, pp. 39-44.
Gnedенко B.V., Fakham G. On a Transfer Theorem // Proceedings of the USSR Academy of Sciences. 1969. Vol. 187. No. 1. pp. 15-17.
Jamirzaev A.A., Mamurov I.N. Transfer Theorems. Monograph, Tashkent “Iqtisod-Moliya” 2019, 148 pp.
Mamurov I. Asymptotic distribution of the central variation members in the case of random sampling volume. Turkish Online Journal of Qualitative Inquiry (TOJQI). Volume 12, Issue 7, July 2021: 4626-4634.
Article Statistics
Downloads
Copyright License
This work is licensed under a Creative Commons Attribution 4.0 International License.