Compound sum distributions (in particular, the classical compound Poisson distribution) assume that claim amounts are independent and independent of the number of claims. These may not be realistic assumptions. In this note, formulas for compound sum distributions are derived for the general case of dependence. The influence of dependence on the distributions is investigated. A data illustration is given.

中文翻译：

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具有相关性的复合和分布

复合总和分布（特别是经典复合泊松分布）假设索赔金额独立于索赔数量。这些可能不是现实的假设。在本说明中，复合和分布的公式是针对一般依赖情况推导出来的。研究了依赖对分布的影响。给出了数据说明。