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

František Rublík

Applications of Mathematics (2001)

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

Abstract

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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.

How to cite

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Rublík, 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 -

References

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  5. Theory of Rank Tests, Academia, Prague, 1967. (1967) MR0229351
  6. Continuous Univariate Distributions, Vol. 1, Wiley & Sons, New York, 1994. (1994) MR1299979
  7. Continuous Univariate Distributions, Vol.  2, Wiley & Sons, New York, 1995. (1995) MR1326603
  8. 10.1080/03610929808832117, Commun. Statist. Theory Methods 27 (1998), 609–633. (1998) MR1619038DOI10.1080/03610929808832117
  9. A quantile goodness-of-fit test applicable to distributions with nondifferentiable densities, Kybernetika 33 (1997), 505–524. (1997) MR1603957
  10. A goodness-of-fit test for Cauchy distribution, In: Probastat ’98, Proceedings of the Third International Conference on Mathematical Statistics, Tatra Mountains Publications, Bratislava, 1999, pp. 71–81. (1999) MR1737694
  11. 10.1093/biomet/52.3-4.591, Biometrika 52 (1965), 591–611. (1965) MR0205384DOI10.1093/biomet/52.3-4.591

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