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 distribution
Poisson distribution
A 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
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
