It was observed that the number of cases and deaths for infectious diseases were associated with heavy-tailed power law distributions such as the Pareto distribution. While Pareto distribution was widely used to model the cases and deaths of infectious diseases, a major limitation of Pareto distribution is that it can only fit a given data set beyond a certain threshold. Thus, it can only model part of the data set. Thus, we proposed some novel discrete composite distributions with Pareto tails to fit the real infectious disease data. To provide necessary statistical inference for the tail behavior of the data, we developed a hypothesis testing procedure to test the tail index parameter. COVID-19 reported cases in Singapore and monkeypox reported cases in France were analyzed to evaluate the performance of the newly created distributions. The results from the analysis suggested that the discrete composite distributions could demonstrate competitive performance compared to the commonly used discrete distributions. Furthermore, the analysis of the tail index parameter can provide great insights into preventing and controlling infectious diseases.

翻译：研究发现，传染病病例数与死亡数通常服从帕累托分布等重尾幂律分布。尽管帕累托分布被广泛用于建模传染病的病例数与死亡数，但其主要局限在于只能拟合超过特定阈值的数据，因此仅能建模部分数据集。为此，我们提出了若干具有帕累托尾部的新型离散复合分布，以拟合真实传染病数据。为对数据尾部行为提供必要的统计推断，我们开发了用于检验尾部指数参数的假设检验方法。通过分析新加坡COVID-19报告病例与法国猴痘报告病例，评估了新构建分布的性能。分析结果表明，与常用离散分布相比，离散复合分布展现出具有竞争力的性能。此外，尾部指数参数的分析可为传染病防控提供重要见解。