Goodness-of-fit tests for the Cauchy distribution
This article presents several modified goodness-of-fit tests for the Cauchy distribution with unknown location and scale parameters. Monte Carlo studies are performed to calculate critical values for several tests based on the empirical distribution function. Power studies suggest that the modified Kuiper (V) test is the most powerful standard test against most alternate distributions over a full range of sample sizes. A reflection technique is also employed which yields substantial improvement in the power of this test against symmetric distributions.
KeywordsCauchy distribution Goodness-of-fit Monte Carlo Kolmogorov-Smirnov test Kuiper test
The authors are grateful to the anonymous reviewers, whose thoughtful suggestions have significantly improved the article.
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