# A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics

Applications of Mathematics (2001)

- Volume: 46, Issue: 5, page 339-351
- ISSN: 0862-7940

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topRublík, František. "A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics." Applications of Mathematics 46.5 (2001): 339-351. <http://eudml.org/doc/33091>.

@article{Rublík2001,

abstract = {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.},

author = {Rublík, František},

journal = {Applications of Mathematics},

keywords = {sample quantiles; chi-squared statistics; goodness-of-fit; Cauchy distribution; sample quantiles; chi-squared statistics; goodness-of-fit, Cauchy distribution},

language = {eng},

number = {5},

pages = {339-351},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics},

url = {http://eudml.org/doc/33091},

volume = {46},

year = {2001},

}

TY - JOUR

AU - Rublík, František

TI - A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics

JO - Applications of Mathematics

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 46

IS - 5

SP - 339

EP - 351

AB - 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.

LA - eng

KW - sample quantiles; chi-squared statistics; goodness-of-fit; Cauchy distribution; sample quantiles; chi-squared statistics; goodness-of-fit, Cauchy distribution

UR - http://eudml.org/doc/33091

ER -

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- 10.1093/biomet/52.3-4.591, Biometrika 52 (1965), 591–611. (1965) MR0205384DOI10.1093/biomet/52.3-4.591

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