New bounds on poisson approximation for random sums of independent negative-binomial randomvariables

Le Truong Giang * and Trinh Huu Nghiem

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

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Received: 11 Feb 2018
Revised: 04 Jun 2018
Accepted: 30 Nov 2018
Published: 03 Nov 2018
DOI: 10.22144/ctu.jen.2018.050
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How to Cite
Le, T. G., & Trinh, H. N. (2018). New bounds on poisson approximation for random sums of independent negative-binomial randomvariables. CTU Journal of Innovation and Sustainable Development , 54(10), 149-153. https://doi.org/10.22144/ctu.jen.2018.050
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No. 10 (2018)

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Abstract

The aim of this paper is to establish new bounds on Poisson approximation for random sums of independent negative-binomial random variables. The bounds showed in current paper are a uniform bound and a non-uniform bound.  The received results in this paper are extensions and generalizations of known results.
Keywords: Negative - binomial variable, Poisson approximation, Random sums, Total variation distance, Uniform and non-uniform bound

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

References

Barbour, A. D., Holst, L. and Janson, S., 1992. Poisson Approximation, Clarendon Press-Oxford, 277.

Kongudomthrap, S. and Chaidee, N., 2012. Bounds in Poisson approximation of random sums of Bernoulli random variables. Journal of Mathematics Research. 4(3): 29-35.

Le Truong Giang and Trinh Huu Nghiem, 2017. Characteristic functions method for some of the limit theorems in probability. Can Tho University Journal of Science. 53: 88-95.

Teerapabolarn, K., 2013a. Improved bounds on Poisson approximation for independent binomial random summands. International Journal of Pure and Applied Mathematics. 89(1): 29-33.

Teerapabolarn, K., 2013b. Poisson approximation for random sums of geometric random variables. International Journal of Pure and Applied Mathematics. 89(1): 35-39.

Teerapabolarn, K., 2014. Poisson approximation for random sums of independent negative binomial random variables. International Journal of Pure and Applied Mathematics. 93(6): 783-787.

Tran Loc Hung and Le Truong Giang, 2014. On bounds in Poisson approximation for integer-valued independent random variables. Journal of Inequalities and Applications, https://doi.org/10.1186/1029-242X-2014-291.

Tran Loc Hung and Le Truong Giang, 2016a. On bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables. SpringerPlus, https://doi.org/10.1186/s40064-016-1710-y.

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

Vellaisamy, P. and Upadhye, S., 2009. Compound negative binomial approximations for sums of random variables. Probability and Mathematical Statistics, 29(2): 205 - 226.

Yannaros, N., 1991. Poisson approximation for random sums of Bernoulli random variables. Statistics & Probability Letters. 11(2): 161-165.