| Title:
|
A quantile goodness-of-fit test for Cauchy distribution, based on extreme order statistics (English) |
| Author:
|
Rublík, František |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
46 |
| Issue:
|
5 |
| Year:
|
2001 |
| Pages:
|
339-351 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
sample quantiles |
| Keyword:
|
chi-squared statistics |
| Keyword:
|
goodness-of-fit |
| Keyword:
|
Cauchy distribution |
| MSC:
|
62G10 |
| MSC:
|
62G30 |
| idZBL:
|
Zbl 1059.62048 |
| idMR:
|
MR1925192 |
| DOI:
|
10.1023/A:1013704326683 |
| . |
| Date available:
|
2009-09-22T18:07:26Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134472 |
| . |
| Reference:
|
[1] R. B. d’Agostino, M. A. Stephens, eds.: Goodness-of-Fit Techniques. Statistics: Textbooks and Monographs, Vol. 68.Marcel Dekker, Inc., New York, 1986. MR 0874534 |
| Reference:
|
[2] V. Barnett, T. Lewis: Outliers in Statistical Data.Wiley & Sons, New York, 1994. MR 1272911 |
| Reference:
|
[3] P. E. Greeenwood, M. S. Nikulin: A Guide to Chi-squared Testing.Wiley & Sons, New York, 1996. MR 1379800 |
| Reference:
|
[4] F. E. Grubbs: Sample criteria for testing outlying observations.Ann. Math. Statistics 21 (1950), 27–58. Zbl 0036.21003, MR 0033993, 10.1214/aoms/1177729885 |
| Reference:
|
[5] J. Hájek, Z. Šidák: Theory of Rank Tests.Academia, Prague, 1967. MR 0229351 |
| Reference:
|
[6] N. L. Johnson, S. Kotz and N. Balakrishnan: Continuous Univariate Distributions, Vol. 1.Wiley & Sons, New York, 1994. MR 1299979 |
| Reference:
|
[7] N. L. Johnson, S. Kotz and N. Balakrishnan: Continuous Univariate Distributions, Vol. 2.Wiley & Sons, New York, 1995. MR 1326603 |
| Reference:
|
[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. MR 1619038, 10.1080/03610929808832117 |
| Reference:
|
[9] F. Rublík: A quantile goodness-of-fit test applicable to distributions with nondifferentiable densities.Kybernetika 33 (1997), 505–524. MR 1603957 |
| Reference:
|
[10] F. Rublík: 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. MR 1737694 |
| Reference:
|
[11] S. S. Shapiro, M. B. Wilk: An analysis of variance test for normality (complete samples).Biometrika 52 (1965), 591–611. MR 0205384, 10.1093/biomet/52.3-4.591 |
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