Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE

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Energy statistics: A class of statistics based on distances (2013, background): “Gurtler and Henze [18], Henze and Zirkler [19], or Matsui and Takemura [31].”
Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms (2007, background): “It is only very recently that Matsui and Takemura (2005) presented sophisticated numerical techniques in determining percentage points for Tβ, for composite goodness–of–fit with Cauchy distributions.”
Goodness-of-fit tests for symmetric stable distributions—Empirical characteristic function approach (2006, methodology): “For past researches on goodness-of-fit tests of heavy-tailed distributions using empirical characteristic function approach, see Gürtler and Henze (2000) and Matsui and Takemura (2005).”