We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable new source of information about the dynamics of the process under study. We show that such behavior can be described only by specific combinations of compound distributions based on the Binomial Distribution and provide their analytical forms which can be used in further investigations and which can be helpful in the analysis of all other types of counting distributions.

中文翻译：

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从组合的角度计算分布

我们从从中提取的组合的角度对计数分布进行了全面的了解。特别是，我们关注这些组合表现出振荡行为的情况，这些行为可以提供有关所研究过程动力学的宝贵新信息来源。我们表明，这种行为只能通过基于二项分布的复合分布的特定组合来描述，并提供它们的分析形式，可用于进一步研究，有助于分析所有其他类型的计数分布。