We give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

中文翻译：

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关于泊松定律的 Rényi-Srivastava 表征的概括

我们为 D. Pierre-Loti-Viaud 和 P. Boulongne 的结果提供了一种新的证明方法，该方法可以看作是对 Rényi 和 Srivastava 的泊松定律表征的概括。我们还根据贝尔多项式提供了明确的公式，用于在非人寿保险的扩展集体模型中出现的复合分布的时刻。