A Test for the Mean in the Zero-Inflated Poisson Distribution

In analyzing Poisson-count data, sometimes a lot of zeros are observed. When there are too many zeros, a zero-inflated Poisson distribution can be a more suitable model to use. A test for the mean θ in the imperfect state can be obtained by using the conditional maximum likelihood estimator θ of θ and the asymptotic variance of θ . For moderately small sample size, the probability of the rejection region under the null hypothesis is found to have only a small variation around the targeted value as the value of the nuisance parameter varies.