Count data are omnipresent in many applied fields, often with overdispersion due to an excess of zeroes or extreme values. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on the challenging problem of identifying a suitable mixing distribution and study how extreme value theory can be used. We propose an original strategy to select the most appropriate candidate among three categories: Fr{\'e}chet, Gumbel and pseudo-Gumbel. Such an approach is presented with the aid of a decision tree and evaluated with numerical simulations.
翻译:计数数据在许多应用领域是无处不在的, 通常由于超过零值或极端值而过于分散。 由于 Poisson 分布的混合物代表着一种优雅和有吸引力的建模战略, 我们在此集中关注一个具有挑战性的问题, 即确定合适的混合分布并研究如何使用极端值理论。 我们提出了一个最初的战略, 选择三类中最合适的候选人: Fr'e}chet、 Gumbel 和伪Gumber。 这种方法是在决策树的帮助下提出的, 并且用数字模拟来评估。