Second order approximations in sequential point estimation of the probability of zero in Poisson distribution

In the analysis of the count data, the Poisson model becomes overtly restrictive in the case of over-dispersed or under-dispersed data. When count data are under-dispersed, specific models such as generalized linear models (GLM) are proposed. Other examples are the zero-inflated Poisson model (ZIP) and zero-truncated Poisson model (ZTP), which have been used in literature to deal with an excess or absence of zeros in count data. Thus having a knowledge of the probability of zeros and its estimation in Poisson distribution can be significant and useful. Some estimation problems with unknown parameter cannot attain minimum risk where the sample size is fixed. To resolve this captivity, working with a sequential sampling procedure can be useful. In this paper, we consider sequential point estimation of the probability of zero in Poisson distribution. Second order approximations to the expected sample size and the risk of the sequential procedure are derived as the cost per observations tends to zero. Finally, a simulation study is given.