Confidence intervals for the difference of means in zero-truncated poisson distributions

A common type of dataset used in applied research is count data. Although occasionally, no zero event is seen in the dataset. The Poisson distribution is inappropriate in this situation then the zero-truncated Poisson distribution is used. Furthermore, applications are interested in the comparison of two population means. Constructing confidence intervals for the mean differences between two zero-truncated Poisson distributions is the purpose of this study. The method of variance of estimates recovery (MOVER) is used. This method takes five methods into consideration when determining the confidence intervals for the single population mean: the Wald method, the score method, the Wald method based on the method of moments estimator, the adjusted Wald method, and the adjusted Wald method based on the method of moments estimator. Its coverage probability is close to the coverage probability level with short expected width in almost all situations in the study. In practice, our methods are confirmed by two application real datasets on the neonatal death and the unrest events in the southern border area of Thailand.