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A study on goodness-of-fit test for extreme value distribution
Journal of the Korean Data & Information Science Society 2019;30:539-49
Published online May 31, 2019;  https://doi.org/10.7465/jkdi.2019.30.3.539
© 2019 Korean Data and Information Science Society.

Byungjin Choi1

1Major in Applied Statistics, Kyonggi University
Correspondence to: Professor, Major in Applied Statistics, Kyonggi University, Suwon-Si, Gyeonggi-Do 16227, Korea. E-mail: bjchoi92@kyonggi.ac.kr
This work was supported by Kyonggi University Research Grant 2016.
Received April 5, 2019; Revised April 30, 2019; Accepted May 13, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The extreme value distribution is extensively used as a probability model for data analysis in various fields including life testing and hydrology. Although the use of the extreme value distribution is theoretically or practically justified in such fields, it is necessary to ascertain the appropriateness of the distribution prior to data analysis. In this paper, we discuss the use of the modified Anderson-Darling and Cramer-von Mises tests of fit for the extreme value distribution with unknown parameters. Since the test statistics to be used include the parameters involved in the extreme value distribution, we present the modified test statistics by replacing the unknown parameters with the estimators obtained by the maximum likelihood method for reducing bias and the maximum entropy method, etc. The critical values of the proposed tests using the modified test statistics are estimated by Monte-Carlo simulations and provided in a tabular form. We also carry out Monte-Carlo simulations for performance comparison in terms of power and present the obtained results.
Keywords : Critical value, EDF test, extreme value distribution, goodness-of-fit, test power, test statistic.