We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests for the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis. The new tests are consistent against a large class of alternatives. A comparative Monte Carlo simulation study shows that the test is a good competitor for the state of the art procedures, and we apply the tests to log-returns of cryptocurrencies.

中文翻译：

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柯西还是非柯西？Cauchy 分布的新拟合优度检验

我们引入了柯西分布的新特征，并为柯西族提出了一类拟合优度检验。极限分布是在原假设下的希尔伯特空间框架中导出的。新测试与一大类替代方案一致。比较蒙特卡洛模拟研究表明，该测试是最先进程序的有力竞争者，我们将测试应用于加密货币的对数回报。