In statistical modeling, it is important to know the mechanisms that cause underdispersion. Several mechanisms that lead to underdispersed count distributions are revisited from new perspectives, and new ones are introduced. These include procedures based on the number of arrivals in arrival processes, such as renewal and pure birth processes and steady-state distributions of birth-death processes, like queues with state-dependent service rates. Weighted Poisson and other well-known underdispersed distributions are also related to birth-death processes. Classical and variable binomial thinning mechanisms are also viewed as important procedures for generating underdispersed distributions, which can also generate bivariate count distributions with negative correlation. Some example applications are shown, one of which is related to Biodosimetry.

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导致分散不足的一些机制：新旧提案

在统计建模中，了解导致欠离散的机制非常重要。从新的角度重新审视导致计数分布不分散的几种机制，并引入新的机制。其中包括基于到达过程中到达数量的程序，例如更新和纯出生过程以及出生-死亡过程的稳态分布，例如具有与状态相关的服务率的队列。加权泊松分布和其他著名的欠分散分布也与出生死亡过程有关。经典和可变二项式细化机制也被视为生成欠分散分布的重要程序，这也可以生成具有负相关性的二元计数分布。显示了一些示例应用，其中之一与生物剂量测定法相关。