Science and Education Publishing
American Journal of Applied Mathematics and Statistics
2328-7292
4
6
2017
1
3
Coincidences, Goodness of Fit Test and Confidence Interval for Poisson Distribution Parameter via Coincidence
185
193
EN
Victor
Nijimbere
School of Mathematics and Statistics, Carleton University, Ottawa, Canada
AJAMS2016464
10.12691/ajams-4-6-4
2016
9
26
2016
10
26
2017
1
1
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: λ1=λ2=….= λn =θ, 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).