Exact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean

ýA Poisson distribution is well used as a standard model for analyzing count dataý. ýSo the Poisson distribution parameter estimation is widely applied in practiceý. ýProviding accurate confidence intervals for the discrete distribution parameters is very difficultý. ýSo farý, ýmany asymptotic confidence intervals for the mean of Poisson distribution is providedý. ýIt is known that the coverage probability of the confidence interval (L(X),U(X)) is a function of distribution parameterý. ýSince Poisson distribution is discreteý, ýcoverage probability of confidence intervals for Poisson mean has no closed form and the exact calculation of confidence coefficientý, ýaverage coverage probability and maximum coverage probabilities for this intervalsý, ýis very difficultý. ýMethodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions with increasing bounds are proposed by Wang (2009)ý. ýIn this paperý, ýwe consider a situation that the both lower and upper bounds of the confidence interval is increasingý. ýIn such situationsý, ýwe explore the problem of finding an exact maximum coverage probabilities for confidence intervals of Poisson meaný. ýDecision about confidence intervals optimalityý, ýbased on simultaneous evaluation of confidence coefficientý, ýaverage coverage probability and maximum coverage probabilitiesý, ýwill be more reliableý.