A Test for the Mean in the Imperfect  State in a Zero-Inflated Poisson Distribution

NIK AHMAD KAMAL AND POOI AH HIN

Research Report No. 15/2001

Abstract

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 $\theta$ in the imperfect state can be obtained by using the estimator $\tilde \theta$ of $theta$ and the asymptotic variance of $\tilde \theta$. For moderately small sample size, the probability of the rejected 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.