Confidence interval for the parameter of the zero-truncated Poisson distribution

Abstract

This paper introduces a confidence interval for the parameter in a zero-truncated Poisson distribution. We adjust the profile likelihood method to construct this confidence interval by using a function of parameter as a nuisance. The performance of the proposed estimator is investigated through simulations, and compared with the conventional Wald confidence interval. From the results, the proposed estimator provides a good performance in terms of coverage probability in all cases in the study. It also has the short interval length. The practicality of our approach is confirmed by application to two real datasets, on a cholera-epidemic and on mortality rates of infants on an estate.