Thời gian: 14h Thứ 5, ngày 17/02/2022

Link online: meet.google.com/nqs-ntdh-wnz

Abstract: Negative binomial random summation is a sum of independent, identically distributed random variables in which a number of the summands in negative binomial distribution. Negative binomial summation is an extension of a geometric sum. Despite the simplicity, such a sum can model many phenomena in queuing, reliability, telecommunications, network analysis, stochastic finance and insurance mathematics, and other real world fields. The main purpose of this talk is to present the characteristics of negative binomial sums with distributions of negative binomial infinitely divisible, and establish the weak limit theorems for negative binomial sums with convergence rates. The presented results in this talk are extensions and generalizations of known ones.

Keywords: Banach’s matchbox problem; Negative binomial random sum; Negative binomial infinite divisibility; Weak limit theorem; Rate of convergence; Trotter’s distance; Zolotarev’s distance. 2000 Mathematics subject classification: 60E07, 60F05, 41A25.

The report is written based on following results of author with colleagues.

1. Tran Loc Hung and Tran Ngoc Hau: On the accuracy of approximation of the distribution of negative binomial random sums by the Gamma distributions. Kybernetika, Vol. 54, N. 5, (2018) 921–936. DOI: 10.14736/kyb-2018-5-0921
2. Tran Loc Hung, Phan Tri Kien, Nguyen Tan Nhut: Asymptotic behaviors with convergence rates of distributions of negative-binomial sums, Science & Technology Development Journal, 22(4), (2019) 415–421. DOI :10.32508/stdj.v22i4.1689
3. Tran Loc Hung and Phan Tri Kien: On the order of approximation in limit theorems for negative binomial sums of strictly stationary m− dependent random variables, Acta Mathematica Vietnamica, 46, (2021) 203–224. DOI: 10.1007/s40306-020-00406-x
4. Tran Loc Hung and Phan Tri Kien: An extension of Zolotarev’s problem ans some related results. Acta Mathematica Scientia, 41B(5): (2021), 1–16. DOI: 10.1007/s10473-021-
5. Tran Loc Hung and Phan Tri Kien: On the rate of convergence in limit theorems for negative binomial random sums. Lobachevskii Journal of Mathematics, Vol. 43, No. 1, (2022) 67–80. DOI: 10.1134/S1995080222010097