Exact Computation of Minimum Sample size for Estimation of Poisson Parameters

In this paper, we develop an approach for the exact determination of the minimum sample size for the estimation of a Poisson parameter with prescribed margin of error and confidence level. The exact computation is made possible by reducing infinite many evaluations of coverage probability to finite many evaluations. Such reduction is based on our discovery that the minimum of coverage probability with respect to a Poisson parameter bounded in an interval is attained at a discrete set of finite many values.

💡 Research Summary

The paper addresses a fundamental problem in statistical inference for Poisson‑distributed data: determining the smallest sample size that guarantees a prescribed absolute error ε and confidence level 1 − δ when estimating the Poisson mean λ. Traditional approaches rely on normal approximations, Chebyshev bounds, or asymptotic formulas, which either over‑estimate the required sample size or fail to provide rigorous guarantees when λ is small or the error tolerance is tight. The authors propose a novel exact method that eliminates the need for approximations by exploiting a structural property of the coverage probability function.

The coverage probability R(λ,n) is defined as the probability that the interval