American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2016, 4(6), 185-193
DOI: 10.12691/ajams-4-6-4
Open AccessArticle

Coincidences, Goodness of Fit Test and Confidence Interval for Poisson Distribution Parameter via Coincidence

Victor Nijimbere1,

1School of Mathematics and Statistics, Carleton University, Ottawa, Canada

Pub. Date: January 03, 2017

Cite this paper:
Victor Nijimbere. Coincidences, Goodness of Fit Test and Confidence Interval for Poisson Distribution Parameter via Coincidence. American Journal of Applied Mathematics and Statistics. 2016; 4(6):185-193. doi: 10.12691/ajams-4-6-4

Abstract

The probability of the coincidence of some discrete random variables having a Poisson distribution with parameters λ1, λ2, …, λn, and moments are expressed in terms of the hypergeometric function 1Fn or the modified Bessel function of the first kind if n=2. Considering the null hypothesis H0: λ12=….= λn, where θ is some positive constant number, asymptotic approximations of the probability and moments are derived for large θ using the asymptotic expansion of the hypergeometric function 1Fn and that of the modified Bessel function of the first kind if n=2. Further, we show that if the sample mean is a minimum variance unbiased estimator (MVUE) for the parameter λi, then the probability that H0 is true can be approximated by that of a coincidence. In that case, a chi-square χ2 goodness of fit test can be established and a 100(1-α)% confidence interval (CI) for θ can be constructed using the variance of the coincidence (or via coincidence) and the Central Limit Theorem (CLT).

Keywords:
probability hypergeometric functions modified bessel functions asymptotic expansion MVUE

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