Abstract

In both flexible Poisson Tweedie (PT) and Poisson-exponential-Tweedie (PET) over-dispersed count models, the common power parameter $p\in \left\{0\right\}\cup [1,\infty )$ works as an automatic distribution selection. It mainly separates two subclasses of zero-inflated ($1\le p<2$) and heavy-tailed (p > 2). Although extensive works have been conducted in discriminating between continuous and semicontinuous distribution functions, not much attention has been paid to discriminating between discrete distribution functions. Estimations based on the likelihood approach for PT and PETs are challenging owing to the presence of an infinity sum and intractable integrals in their probability mass functions. Thus, we attempt to perform a Monte Carlo simulation to approximate them. In this paper, we invest the ratio of the maximized likelihoods within each subclass of these two models for discrimination purposes based on classic measures of dispersion, zero-inflation and heavy tail of both PT and PET models. Grounded only on dispersion index, we also discriminate two particular cases of the Hermite distribution with respect to its geometric version (p = 0) and the negative binomial one with its geometric version (p = 2). Probabilities of correct selection for several combinations of dispersion parameters, means and sample sizes are examined by simulations. We carry out a numerical comparison study to assess the discrimination procedures in these subclasses of two families.

摘要

在灵活的 Poisson Tweedie (PT) 和 Poisson-exponential-Tweedie (PET) 过度分散计数模型中，公共功率参数$p\in \left\{0\right\}\cup [\mathrm{1个},\infty )$用作自动分布选择。它主要分离了零膨胀的两个子类（$\mathrm{1个}\le p<\mathrm{2个}$) 和重尾 ( p > 2). 尽管在区分连续和半连续分布函数方面进行了大量工作，但对区分离散分布函数的关注却很少。由于 PT 和 PET 的概率质量函数中存在无穷和和难以处理的积分，基于 PT 和 PET 的似然法的估计具有挑战性。因此，我们尝试执行蒙特卡罗模拟来近似它们。在本文中，我们基于 PT 和 PET 模型的分散、零膨胀和重尾的经典度量，在这两个模型的每个子类中投资最大似然率以用于区分目的。仅基于色散指数，我们还根据其几何版本区分了 Hermite 分布的两种特殊情况（p  = 0) 和负二项式及其几何版本 ( p  = 2)。通过模拟检查正确选择分散参数、均值和样本大小的几种组合的概率。我们进行了一项数值比较研究，以评估两个家庭的这些子类中的歧视程序。