论文标题
灵活的模型，用于过度分散和分散的计数数据
Flexible models for overdispersed and underdispersed count data
论文作者
论文摘要
在过度分散计数数据的概率模型的框架内，我们提出了广义分数泊松分布（GFPD），这是分数泊松分布（FPD）的自然概括（FPD）和标准泊松分布。我们得出了GFPD的某些特性，更具体地说，我们研究了时刻，限制了FPD的行为和其他特征。偏斜表明可以将FPD左旋转，右旋转或对称。这使得模型在实践中具有灵活性和吸引力。我们将模型应用于实际的大计数数据，并使用最大可能性估算模型参数。然后，我们转向非常一般的加权泊松分布（WPD）类别，以使过度分散和分散不足。与KEMP的广义超几何概率分布相似，该分布基于超几何函数，我们分析了一类WPD与Mittag-Leffler函数的概括相关。提出的一类分布包括众所周知的Com-Poisson和Hyper-Poisson模型。我们表征了允许过度分散和分散不足的参数的条件，并分析了文献中尚未出现的两个特殊案例。
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD's) to allow both overdispersion and underdispersion. Similarly to Kemp's generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD's related to a generalization of Mittag--Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.
