We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an empirical weight function which is compared to its theoretical counterpart under the Poisson assumption. Weighted Lp distances between these empirical and theoretical functions are proposed as test statistics and closed form expressions are derived for L1, L2 and L1 distances. A Monte Carlo study is included in which the newly proposed tests are shown to be powerful when compared to existing tests, especially in the case of overdispersed alternatives. We demonstrate the use of the tests with two practical examples.

翻译：我们提出了适用于泊松分布的新拟合优度检验方法。该检验过程通过将加权泊松分布（其中泊松分布作为其特例）拟合至观测数据，并基于样本数据计算经验权重函数，进而将其与泊松分布假设下的理论权重函数进行比较。我们提出将经验函数与理论函数之间的加权Lp距离作为检验统计量，并推导了L1、L2及L1距离的闭式表达式。蒙特卡洛研究表明，与现有检验方法相比，所提出的新检验在检验功效上表现更优，尤其针对过离散备择假设情形。最后通过两个实际案例展示了该检验方法的应用。