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

翻译：我们引入了对Cauchy分布的新的定性,并向Cauchy家庭提出了一类健康测试。限制分布来自Hilbert空间框架的无效假设和固定的替代物。新的测试与一大批替代物是一致的。一个比较的Monte Carlo模拟研究表明,该测试对最新工艺程序具有竞争力,我们对加密的日志回报进行测试。