Duration Dependence and Dispersion in Count-Data Models
探讨事件间等待时间非指数分布与固定时间内事件计数分布的关系，发现等待时间风险函数递减导致过度离散、递增导致不足离散，并基于伽马分布假设推导新计数模型，应用于出生数和医生咨询数。
This paper explores the relation between non-exponential waiting times between events and the distribution of the number of events in a fixed time interval. It is shown that within this framework the frequently observed phenomenon of overdispersion, i.e. a variance that exceeds the mean, is caused by a decreasing hazard function of the waiting times, while an increasing hazard function leads to underdispersion. Using the assumption of i.i.d. gamma distributed waiting times, a new count data model is derived. Its use is illustrated in two applications: the number of births, and the number of doctor consultations.