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A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics
Applications of Mathematics, Tome 46 (2001) no. 5, pp. 339-351 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A test statistic for testing goodness-of-fit of the Cauchy distribution is presented. It is a quadratic form of the first and of the last order statistic and its matrix is the inverse of the asymptotic covariance matrix of the quantile difference statistic. The distribution of the presented test statistic does not depend on the parameter of the sampled Cauchy distribution. The paper contains critical constants for this test statistic, obtained from $50\,000$ simulations for each sample size considered. Simulations show that the presented test statistic is for testing goodness-of-fit of the Cauchy distributions more powerful than the Anderson-Darling, Kolmogorov-Smirnov or the von Mises test statistic.
A test statistic for testing goodness-of-fit of the Cauchy distribution is presented. It is a quadratic form of the first and of the last order statistic and its matrix is the inverse of the asymptotic covariance matrix of the quantile difference statistic. The distribution of the presented test statistic does not depend on the parameter of the sampled Cauchy distribution. The paper contains critical constants for this test statistic, obtained from $50\,000$ simulations for each sample size considered. Simulations show that the presented test statistic is for testing goodness-of-fit of the Cauchy distributions more powerful than the Anderson-Darling, Kolmogorov-Smirnov or the von Mises test statistic.
DOI : 10.1023/A:1013704326683
Classification : 62G10, 62G30
Keywords: sample quantiles; chi-squared statistics; goodness-of-fit; Cauchy distribution 
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     title = {A quantile goodness-of-fit test for {Cauchy} distribution, based on extreme order statistics},
     journal = {Applications of Mathematics},
     pages = {339--351},
     year = {2001},
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Rublík, František. A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics. Applications of Mathematics, Tome 46 (2001) no. 5, pp. 339-351. doi: 10.1023/A:1013704326683

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