Volume 68 | Issue 9 | Year 2022 | Article Id. IJMTT-V68I9P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I9P501

Received | Revised | Accepted | Published |
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18 Jul 2022 | 19 Aug 2022 | 01 Sep 2022 | 10 Sep 2022 |

This paper uses the Stein-Chen method to obtain an improved bound on the Poisson approximation under the restriction of Poisson mean λ=1. In addition, it indicated that the bound in this study is better than that reported in Teerapabolarn [21].

[1] A. D. Barbour, L. Holst and S. Janson, “Poisson Approximation,” (Oxford Studies in Probability 2), Clarendon Press, Oxford, 1992.

[2] L. H. Y. Chen, “Poisson Approximation for Dependent Trials,” Annals of Probability, vol. 3, no. 3, pp. 534-545, 1975.

[3] R. Kun and K. Teerapabolarn, “A Pointwise Poisson Approximation By W-Functions,” Applied Mathematical Sciences, vol. 6, no. 101, pp. 5029-5037, 2012.

[4] K. Lange, “Applied Probability,” Springer, New York, 2003.

[5] M. Majsnerowska “A Note on Poisson Approximation By W-Functions,” Applicationes Mathematicae, vol. 25, no. 3, pp. 387-392, 1998.

[6] V. G. Mikhailov, “On a Poisson Approximation for the Distribution of the Number of Empty Cells in a Nonhomogeneous Allocation Scheme,” Theory of Probability & Its Applications, vol. 42, no. 1, pp. 184-189, 1998.

[7] K. Neammanee, “Pointwise Approximation of Poisson Binomial By Poisson Distribution,” Stochastic Modelling and Applications, vol. 6, no. 1, pp. 20-26, 2003.

[8] K. Neammanee, “Non-Uniform Bound for the Approximation of Poisson Binomial By Poisson Distribution,” International Journal of Mathematics and Mathematical Sciences, vol. 48, no. 1, pp. 3041-3046, 2003

[9] C. M. Stein, “A Bound for the Error in Normal Approximation to the Distribution of a Sum of Dependent Random Variables”, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, California, vol. 2, pp. 583-602, 1972.

[10] C. M. Stein, “Approximate Computation of Expectations,” Hayward, Ca:Ims, 1986.

[11] K. Teerapabolarn, “A Non-Uniform Bound on Poisson Approximation for Sums of Bernoulli Random Variables with Small Mean,”

Thai Journal of Mathematics, vol. 4, no. 1, pp. 179-196, 2006.

[12] K. Teerapabolarn, “A Non-Uniform Bound in Probability Approximation Via the Stein-Chen Method,” Stochastic Modelling and Applications, vol. 9, no. 1, pp. 1-15, 2006.

[13] K. Teerapabolarn, “A Bound on the Poisson-Binomial Relative Error,” Statistical Methodology, vol. 4, no. 4, pp. 407-415, 2007.

[14] K. Teerapabolarn, “Bounds on Approximating the Yule Distribution By the Poisson and Geometric Distributions,” International Journal of Applied Mathematics & Statistics, vol. 14, no. 9, pp. 86-93, 2009.

[15] K. Teerapabolarn, “A Poisson-Binomial Relative Error Uniform Bound,” Statistical Methodology, vol. 7, no. 2, pp. 69-76, 2010.

[16] K. Teerapabolarn, “on the Poisson Approximation to the Negative Hypergeometric Distribution,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 34, no. 2, pp. 331-336, 2011.

[17] K. Teerapabolarn, “An Improvement of Bound on the Poisson-Binomial Relative Error,” International Journal of Pure and Applied Mathematics, vol. 80, no. 5, pp. 711-719, 2012.

[18] Teerapabolarn, “A Non-Uniform Bound on the Poisson-Negative Binomial Relative Error,” General Mathematics Notes, vol. 12, no. 2, pp. 1- 9, 2012.

[19] K. Teerapabolarn, “An Improvement of Poisson Approximation for Sums of Dependent Bernoulli Random Variables,” Communications in Statistics—Theory and Methods, vol. 43, no. 8, pp. 1758-1777, 2014.

[20] K. Teerapabolarn, “New Non-Uniform Bounds on Poisson Approximation for Dependent Bernoulli Trials,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 38, no. 1, pp. 231-248, 2015.

[21] K. Teerapabolarn, “Improvements of Poisson Approximation for N-Dimensional Unit Cube Random Graph,” Songklanakarin Journal of Science & Technology, vol. 43, no. 4, pp. 917-926, 2021.

[22] K. Teerapabolarn and K. Neammanee, “A Non-Uniform Bound on Poisson Approximation in Somatic Cell Hybrid Model,” Mathematical Biosciences, vol. 195, no. 1, pp. 56-64, 2005.

[23] K. Teerapabolarn and K. Neammanee, “A Non-Uniform Bound on Poisson Approximation for Dependent Trials,” Stochastic Modelling and Applications, vol. 8, no. 1, pp. 17-31, 2005.

[24] K. Teerapabolarn and K. Neammanee, “Poisson Approximation for Sums of Dependent Bernoulli Random Variables,” Acta Mathematica Academiae Paedagogicae Ny´Iregyh´Aziensis, vol. 22, no. 1, pp. 87-99, 2006.

[25] K. Teerapabolarn and K. Neammanee, “A Non-Uniform Bound on Matching Problem,” Kyungpook Mathematical Journal, vol. 46, no. 4, pp. 489-496, 2006.

[26] K. Teerapabolarn and T. Santiwipanont, “Two Non-Uniform Bounds in the Poisson Approximation of Sums of Dependent Indicators,” Thai Journal of Mathematics, vol. 5, no. 1, pp. 15-39, 2007.

[27] P. Wongkasem, K. Teerapabolarn and R. Gulasirima, “on Approximating A Generalized Binomial and Poisson Distributions,” International Journal of Statistics and Systems, vol. 3, no. 2, pp. 113-124, 2008.

Kanint Teerapabolarn, "An Improved Bound on Poisson Approximation for the Poisson Mean λ=1 with Stein-Chen Method," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 68, no. 9, pp. 1-4, 2022. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V68I9P501