A weak law of large numbers and Poisson approximation problem for extension random sums of m-dependent random variables

Le Truong Giang * and Trinh Huu Nghiem

* Corresponding author (ltgiang@ufm.edu.vn)

Article Sidebar

Full Text: PDF

Received: 21 Jun 2018
Revised: 15 Sep 2018
Accepted: 29 Mar 2019
Published: 30 Mar 2019
DOI: 10.22144/ctu.jen.2019.014
Views
145
Downloads
58
Crossref
Scopus
Google Scholar
Europe PMC
How to Cite
Le, T. G., & Trinh, H. N. (2019). A weak law of large numbers and Poisson approximation problem for extension random sums of m-dependent random variables. CTU Journal of Innovation and Sustainable Development , 11(1), 100-103. https://doi.org/10.22144/ctu.jen.2019.014
Issue
Vol. 11 No. 1 (2019)

Main Article Content

Abstract

In probability theory, Limit theorems are often considered for independent random variables. These results have been applied in many fields. However, there are several studied models presented that random variables depend on each other. The aim of current paper is to study an extension of random sums of m - dependent random variables. Weak law of large numbers and Poisson approximation problem for random sums are established. The received results are extensions and generalizations of some known results.
Keywords: Limit theorems, m–dependent, Poisson approximation, Random sums, Weak Law of Large Numbers

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

References

Dianada, P. H., 1955. The central limit theorem for m-dependent variables. Mathematical Proceedings of the Cambridge Philosophical Society, 51(1): 92-95.

Hoffding, W. and Robbins H., 1948. The central limit theorem for dependent variables. Duke Math. J. 15(1): 773 -780.

Islak, U., 2016. Asymptotic results for random sums of dependent random variables. Statistics and Probability Letters. 109(1): 22-29.

Le Truong Giang and Tran Loc Hung, 2018. An extension of random summations of independent and identically distributed random variables, Commun. Korean Math. Soc. 33(2): 605-618.

Shang, Y., 2012. A central limit theorem for randomly indexed m-dependent random variables. Filomat. 26(4): 713-717.

Tran Loc Hung and Le Truong Giang, 2016. On the bounds in Poisson approximation for independent geometric distributed random variables, Bulletin of the Irannian Mathematical Society. 42(5): 1087-1096.

Van der Genugten, B. B., 1989. A weak law of large numbers for m-dependent random variables with unbounded M. (Research memorandun/ Tilburg University, Department of Economics, Vol. FEW 412).