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首页> 外文会议>Transportation Research Board Annual meeting >Over- and Under-Dispersed Count Data:Comparing the Conway-Maxwell-Poisson and Double-Poisson Distributions
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Over- and Under-Dispersed Count Data:Comparing the Conway-Maxwell-Poisson and Double-Poisson Distributions

机译：过度分散和分散不足的计数数据：比较Conway-Maxwell-Poisson和Double-Poisson分布

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Crash data have often been shown to exhibit over-dispersion, which means that the samplevariance is greater than the sample mean. On rare occasions, this kind of data has been found tobe characterized by under-dispersion. In order to handle under-dispersion, researchers in variousfields have proposed alternative distributions or models. Of all the available distributions thathave been proposed in the literature, two distributions that can handle both over- and underdispersionare of interest: the Conway-Maxwell-Poisson (COM-Poisson) and the Double-Poisson(DP) distributions. The properties of the COM-Poisson have been investigated extensively byvarious researchers but not for the DP, although the latter one has been introduced over 25 yearsago. The primary objective of this paper was to examine the potential applicability of the DPdistribution for analyzing crash data characterized by both over- and under-dispersion. The studyobjective was accomplished using simulated data for nine different mean-dispersion relationships(or scenarios). The DP distribution was compared with the COM-Poisson distribution. Thesimulation results showed that the COM-Poisson performed better than DP for all nine scenariosand that DP worked better for high mean scenarios independent of the type of dispersion.Overall, since the differences observed in statistical fit between the two distributions is moreimportant for under-dispersed datasets, there may not be any need to forgo the COM-Poisson forthe DP for analyzing datasets characterized by under-dispersion.
机译：碰撞数据通常显示出过度分散，这意味着样品 方差大于样本均值。在极少数情况下，已发现此类数据可以 特点是分散不足。为了应对色散，研究人员在各种 领域已经提出了替代的分布或模型。在所有可用的发行版中 在文献中已经提出了两种可以同时处理过度分散和分散不足的分布 很有意思：康威-麦克斯韦-泊松（COM-Poisson）和双泊松 （DP）分布。 COM-Poisson的性质已被广泛研究 各种研究人员，但不是针对DP的，尽管后者已经引入了25年 前。本文的主要目的是研究DP的潜在适用性 用于分析以过度分散和分散不足为特征的崩溃数据的分布。研究 使用九种不同均值-色散关系的模拟数据完成了目标 （或方案）。将DP分布与COM-Poisson分布进行了比较。这 仿真结果表明，在所有九种情况下，COM-Poisson的性能均优于DP。 并且DP在与分散类型无关的高均值情况下效果更好。 总体而言，由于两种分布在统计拟合中观察到的差异更大 对于分散性较低的数据集很重要，可能不需要放弃COM-Poisson 用于分析以色散不足为特征的数据集的DP。

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