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

Bruno Ebner (), Lena Eid and Bernhard Klar ()
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Bruno Ebner: Karlsruhe Institute of Technology (KIT)
Lena Eid: Karlsruhe Institute of Technology (KIT)
Bernhard Klar: Karlsruhe Institute of Technology (KIT)

Statistical Papers, 2024, vol. 65, issue 1, No 3, 45-78

Abstract: Abstract 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.

Keywords: Goodness-of-fit; Cauchy distribution; Hilbert-space valued random elements; Primary 62G10; Secondary 62E10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-022-01382-0

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