A consistent test based on the probability generating function is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted alternatives to the Poisson distribution. The statistic, in addition to have an intuitive and simple form, is asymptotically normally distributed, allowing a straightforward implementation of the test. The finite sample properties of the test are investigated by means of an extensive simulation study. The test shows a satisfactory behaviour compared to other tests with known limit distribution.

翻译：根据概率产生功能,建议进行一致的测试,以便对照广泛的计数分布类别评估 Poisson 特性,其中包括一些最经常采用的Poisson分布的替代方法,该统计数据除了具有直观和简单的形式外,还通常不时地分布,从而可以直接执行该测试。通过广泛的模拟研究对试验的有限样本特性进行调查。该测试显示与其他已知限制分布的测试相比,行为令人满意。