Efficient monitoring of overdispersed counts with time-varying population sizes

Abstract

The monitoring of count data is a major issue in many industrial applications and research activities. Count data often exhibit overdispersion with variance greater than mean, which makes the commonly used Poisson distribution problematic because of its underlying assumption of equal mean and variance. In this article, we consider the surveillance strategy for overdispersed count data, and we also take into account the effect of time-varying population sizes. In particular, to model the data we propose to adapt the generalized Poisson distribution to incorporate the incidence rate, the overdispersion factor, and the non-constant population sizes. The weighted likelihood ratio test is employed for online monitoring. Simulations show that the proposed method is efficient at detecting changes simultaneously in both the incidence rate and the overdispersion factor, and it is robust under different time-varying patterns of the population sizes.