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Goodness-of-fit test for the gumbel distribution based on the generalized Lorenz curve
Journal of the Korean Data & Information Science Society 2017;28:733-42
Published online July 31, 2017
© 2017 Korean Data & Information Science Society.

Kyeongjun Lee1

1Department of Computer Science and Statistics, Daegu University
Correspondence to: Kyeongjun Lee
Assistant professor, Department of Computer Science and Statistics, Daegu University, Gyeongsan 38453, Korea. E-mail: leekj@daegu.ac.kr
Received June 29, 2017; Revised July 11, 2017; Accepted July 13, 2017.
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
There are many areas of applications where Gumbel distribution are employed such as environmental sciences, system reliability and hydrology. The goodness-of-fit test for Gumbel distribution is very important in environmental sciences, system reliability and hydrology data analysis. Therefore, we propose the two test statistics to test goodnessof- fit for the Gumbel distribution based on the generalized Lorenz curve. We compare the new test statistic with the Anderson - Darling test, Cramer - vonMises test, and modified Anderson - Darling test in terms of the power of the test through by Monte Carlo method. As a result, the new test statistics are more powerful than the other test statistics. Also, we propose new graphic method to goodness-of-fit test for the Gumbel distribution based on the generalized Lorenz curve.
Keywords : Generalized Lorenz curve, goodness-of-fit test, Gumbel distribution, Lorenz curve, power