caa a22 4500 475826949 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1004113805623 doi (NATIONALLICENCE)springer-10.1023/A:1004113805623 Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function [Elektronische Daten] [Nora Gürtler, Norbert Henze] Let X 1,...,X n be independent observations on a random variable X. This paper considers a class of omnibus procedures for testing the hypothesis that the unknown distribution of X belongs to the family of Cauchy laws. The test statistics are weighted integrals of the squared modulus of the difference between the empirical characteristic function of the suitably standardized data and the characteristic function of the standard Cauchy distribution. A large-scale simulation study shows that the new tests compare favorably with the classical goodness-of-fit tests for the Cauchy distribution, based on the empirical distribution function. For small sample sizes and short-tailed alternatives, the uniformly most powerful invariant test of Cauchy versus normal beats all other tests under discussion. The Institute of Statistical Mathematics, 2000 Goodness-of-fit test nationallicence Cauchy distribution nationallicence empirical characteristic function nationallicence kernel transformed empirical process nationallicence stable distribution nationallicence uniformly most powerful invariant test nationallicence Gürtler Nora Institut für Mathematische Stochastik, Universität Karlsruhe, Englestr. 2, 76128, Karlsruhe, Germany aut Henze Norbert Institut für Mathematische Stochastik, Universität Karlsruhe, Englestr. 2, 76128, Karlsruhe, Germany aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 267-286 0020-3157 52:2<267 2000 52 10463 https://doi.org/10.1023/A:1004113805623 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004113805623 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gürtler Nora Institut für Mathematische Stochastik, Universität Karlsruhe, Englestr. 2, 76128, Karlsruhe, Germany aut NATIONALLICENCE 700 1- Henze Norbert Institut für Mathematische Stochastik, Universität Karlsruhe, Englestr. 2, 76128, Karlsruhe, Germany aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 267-286 0020-3157 52:2<267 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer