A flexible distribution class for count data
A flexible distribution class for count data
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计数数据的灵活分布类
DOI：
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发表时间：
2017
影响因子：
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通讯作者：
K. Weems
中科院分区：
文献类型：
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作者：
Kimberly F. Sellers;Andrew W. Swift;K. Weems
泊松分布、几何分布和伯努利分布是灵活计数分布的特殊情况，即康韦-麦克斯韦-泊松（CMP）分布-泊松分布的两参数推广，可以适应数据过度分散或分散不足。这项工作进一步概括了CMP分布的思想，通过考虑CMP随机变量的总和来建立一个灵活的分布类，包括泊松分布，负二项分布和二项分布作为特殊情况。这个Conway-Maxwell-Poissons（sCMP）类捕获了CMP及其特殊情况，以及经典的负二项分布和二项分布。通过模拟和真实的数据的例子，我们证明了这个模型的灵活性，包括几个经典的分布以及其他计数数据分布包含显着的数据分散。
The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-parameter generalization of the Poisson distribution that can accommodate data over- or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model’s flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion.