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A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics. (English) Zbl 1059.62048
The author presents a test statistic for testing goodness-of-fit of the Cauchy distribution. This statistic has the shape of a quadratic form of the first and the last order statistic and its distribution does not depend on the real parameter of the sampled Cauchy distribution. Critical constants for this test statistic are evaluated on the basis of 50 000 simulations for each considered sample size. A simulation study is done to compare this test statistic with the Anderson-Darling, Kolmogorov-Smirnov and the von Mises test statistics in the sense of their powers under several alternatives. Results for the considered alternatives show that the presented test statistic is more powerful for testing the goodness-of-fit of the Cauchy distribution than the other mentioned statistics.

MSC:
62G10 Nonparametric hypothesis testing
62G30 Order statistics; empirical distribution functions
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[1] R. B. d’Agostino, M. A. Stephens: Goodness-of-Fit Techniques. Statistics: Textbooks and Monographs, Vol. 68. Marcel Dekker, Inc., New York, 1986.
[2] V. Barnett, T. Lewis: Outliers in Statistical Data. Wiley & Sons, New York, 1994. · Zbl 0801.62001
[3] P. E. Greeenwood, M. S. Nikulin: A Guide to Chi-squared Testing. Wiley & Sons, New York, 1996. · Zbl 0853.62037
[4] F. E. Grubbs: Sample criteria for testing outlying observations. Ann. Math. Statistics 21 (1950), 27-58. · Zbl 0036.21003
[5] J. Hájek, Z. Šidák: Theory of Rank Tests. Academia, Prague, 1967. · Zbl 0161.38102
[6] N. L. Johnson, S. Kotz and N. Balakrishnan: Continuous Univariate Distributions, Vol. 1. Wiley & Sons, New York, 1994. · Zbl 0811.62001
[7] N. L. Johnson, S. Kotz and N. Balakrishnan: Continuous Univariate Distributions, Vol. 2. Wiley & Sons, New York, 1995. · Zbl 0821.62001
[8] M. Menéndez, D. Morales, L. Pardo and I. Vajda: Two approaches to grouping of data and related disparity statistics. Commun. Statist. Theory Methods 27 (1998), 609-633. · Zbl 1126.62300
[9] F. Rublík: A quantile goodness-of-fit test applicable to distributions with nondifferentiable densities. Kybernetika 33 (1997), 505-524. · Zbl 0930.62015
[10] F. Rublík: A goodness-of-fit test for Cauchy distribution. Probastat ’98, Proceedings of the Third International Conference on Mathematical Statistics, Tatra Mountains Publications, Bratislava, 1999, pp. 71-81. · Zbl 0986.62035
[11] S. S. Shapiro, M. B. Wilk: An analysis of variance test for normality (complete samples). Biometrika 52 (1965), 591-611. · Zbl 0134.36501
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