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A Note on A New Improved Poisson Distribution and Its Approximations

Samson O. Egege, Bright O. Osu and Emmanuel Inyang

Abstract

This work, determine a new improved Poisson distribution with mean ? = ?? ? from Polya distribution with parameters ?, ?, ? and ? where ?, ?, ? ??? ? are non-negative integer. It was found that the new improved Poisson approximates binomial distribution accurately more than the normal Poisson for ? so large and ? ?+? sufficient small for ? ? {0,1 … ?} while the new improved Poisson approximates Polya distribution for a certain random variable? ? ? {0.1}, provided that ? is not large enough. This implies the new improved Poisson distribution is not sufficient to enough to approximate Polya distribution

Keywords

- Binomial distributionPoisson distributionA new Improved Poisson

References

[1] Bright O.Osu ,Samson O.Egege and Silas Ihedioha “Option Evaluation : Black Scholes Model versus Improved Poisson Model in Option Pricing” Transaction on Nigeria Association of Mathematics Physics (NAMP) vol7, pp55-62, 2016 [2] Dongping Hu, Yongquan Cui, and Aihua Yin “An improved Negative Binomial Approximation for Negative Hypergeometric Distribution”, Applied Mechanice and Material, vol 427-429,pp 106-110,2013 [3] Samson O.Egege ,Bright O. Osu and Emmanuel J. Ekpeyong “Application of generalized Binomial model in option pricing ,American Journal of Applied Mathematics and Statistics ,vol5, N0 2 pp 62-71, 2017 [4] Samson O. Egege , Bright .O. Osu and Chigozie Chibuisi “An Improved Poisson Distribution and Its Application in Option Pricing” , Open Science Journal of Mathematics and Application vol 6, No3 pp 15-22 ,2018 [5] Samson O. Egege ,Bright O.Osu and Chigozie Chibuisi “A non Uniform bound approximation of Polya via Poisson , using Stein’s Chen method and w-function and its application in option pricing”, International journal of Mathematics and Statistics Invention vol 6.Issue 3 pp 09-20, 2018 [6] Samson O. Egege , Bright O. Osu , Kingsley Uchendu and Chiemela B. Akachi “An improved Poisson approximation for the generalized Binomial distribution with financial Application” Elixir International journal of Applied Mathematics , 121, pp 51509-51519 , 2018 [7] Samson O.Egege, Bright O. Osu and Chogozie Chibuisi. “A non- uniform bound approximation of Pólya via Poisson,Using ,Stein –Chen method and ?- function and its application in option pricing”. International journal of Mathematics and Statistics Invention (IJMSI) Vol 6 Issue 3 ,PP 09-20, 2018 [8] Teerapabolarn K. and Jaioun K. “A improved Poisson Approximation for Binomial Distribution “Applied Mathematics Sciences , vol 8, no 174,pp 8651-8654,2014 [9] Teerapabolarn K “Approximation of Binomial Distribution by an Improved Poisson Distribution” International Journal of Pure and Applied Mathematics vol 97,n0 4 pp 491-495 , 2014 [10] Teerapabolarn K “An improved Poisson Aproximation to Binomial Distribution” International journal of Mathematics Trend and Technology , vol 68,issue 9, pp16-20 ,2022 [11] Teerapabolarn K “Binomial Approximation to the Polya Distribution” international journal of Pure and Applied Mathematics ,vol 78 N0.5 pp 635-640 , 2012

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