The geometric distribution is one of the most widely used count distributions. Novel goodness of fit tests for this distribution are suggested taking advantage of a characterization of that distribution in terms of a differential equation involving its probability generating function. Several ways of looking at the characterization allow us to derive six test statistics. The connection between some of these test statistics and the ratio-plot device is stated. The asymptotic null distributions of these test statistics are derived. However, they depend on the unknown parameter of the geometric law. A suitable parametric bootstrap is used to estimate consistently each null distribution. Moreover, the almost sure limits of the test statistics under alternatives are obtained. The finite sample performance of the bootstrap approximation is assessed via simulation. The powers of the new tests are numerically compared with that of some existing ones, exhibiting competitive behaviour. Some real-life data set applications are included.

几何分布是最广泛使用的计数分布之一。建议利用该分布在涉及其概率生成函数的微分方程方面的表征来对该分布进行新的拟合优度检验。查看特征的几种方法使我们能够得出六个测试统计数据。陈述了其中一些测试统计量与比率绘图设备之间的联系。导出这些检验统计量的渐近零分布。然而，它们取决于几何定律的未知参数。使用合适的参数引导程序来一致地估计每个零分布。此外，获得了在替代方案下测试统计的几乎确定的限制。Bootstrap 近似的有限样本性能是通过模拟来评估的。新测试的能力与一些现有测试的能力进行了数值比较，表现出竞争行为。包括一些现实生活中的数据集应用程序。