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.

中文翻译：

---

有效监测随时间变化的人口规模的过度分散计数

摘要 计数数据的监控是许多工业应用和研究活动中的一个主要问题。计数数据经常表现出方差大于均值的过度离散，这使得常用的泊松分布存在问题，因为它的基本假设是均值和方差相等。在本文中，我们考虑了过度分散计数数据的监视策略，并且我们还考虑了随时间变化的人口规模的影响。特别是，为了对数据进行建模，我们建议调整广义泊松分布以纳入发病率、过度分散因子和非常数的人口规模。在线监测采用加权似然比检验。