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arXiv · 2106.13073

Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution

Bruno Ebner·Lena Eid·Bernhard Klar
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Abstract

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.

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Bruno Ebner, Lena Eid, Bernhard Klar. 2021-06-24. Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution. https://arxiv.org/abs/2106.13073

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