We factorize probability mass functions of discrete distributions belonging to Panjer’s family and to its certain extensions to define a stochastic order on the space of distributions supported on \({\mathbb {N}}_0\). Main properties of this order are presented. Comparison of some well-known distributions with respect to this order allows to generate new families of distributions that satisfy various recurrrence relations. The recursion formula for the probabilities of corresponding compound distributions for one such family is derived. Applications to various domains of reliability theory are provided.

中文翻译：

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关于由 Panjer 离散分布家族的扩展引起的随机顺序

我们分解属于 Panjer 家族及其某些扩展的离散分布的概率质量函数，以在\({\mathbb {N}}_0\)上支持的分布空间上定义随机顺序。介绍了此订单的主要属性。关于这个顺序的一些众所周知的分布的比较允许生成满足各种递归关系的新分布族。推导出了一个此类族的相应化合物分布概率的递归公式。提供了在可靠性理论各个领域的应用。