@article{ajams2016464,
author={Nijimbere, Victor},
title={Coincidences, Goodness of Fit Test and Confidence Interval for Poisson Distribution Parameter via Coincidence},
journal={American Journal of Applied Mathematics and Statistics},
volume={4},
number={6},
pages={185--193},
year={2016},
url={http://pubs.sciepub.com/ajams/4/6/4},
issn={2328-7292},
abstract={The probability of the coincidence of some discrete random variables having a Poisson distribution with parameters *¦Ë*_{1}*,** **¦Ë*_{2}*,** **¡, ¦Ë*_{n}, and moments are expressed in terms of the hypergeometric function _{1}*F*_{n} or the modified Bessel function of the first kind if *n=2*. Considering the null hypothesis *H*_{0}*: ¦Ë*_{1}*=¦Ë*_{2}*=¡.= ¦Ë*_{n}* =¦È*, where *¦È* is some positive constant number, asymptotic approximations of the probability and moments are derived for large *¦È* using the asymptotic expansion of the hypergeometric function _{1}*F*_{n} 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 *¦Ë*_{i}, then the probability that *H*_{0} is true can be approximated by that of a coincidence. In that case, a chi-square *¦Ö*^{2 }goodness of fit test can be established and a 100(1-*¦Á*)% confidence interval (CI) for *¦È* can be constructed using the variance of the coincidence (or via coincidence) and the Central Limit Theorem (CLT).},
doi={10.12691/ajams-4-6-4}
publisher={Science and Education Publishing}
}