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Hypothesis tests of goodness-of-fit for Fréchet distribution

Extreme Value Theory (EVT) is a statistical field whose main focus is to investigate extreme phenomena. In EVT, Fréchet distribution is one of the extreme value distributions and it is used to model extreme events. The degree of fit between the model and the observed values was measured by Goodness-...

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Main Authors: Zainal Abidin, Nahdiya, Adam, Mohd Bakri, Midi, Habshah
Format: Article
Language:English
Published: Universiti Putra Malaysia Press 2014
Online Access:http://psasir.upm.edu.my/id/eprint/40617/1/100.%20Hypothesis%20Tests%20of%20Goodness-of-Fit%20for%20Fr%C3%A9chet%20Distribution.pdf
http://psasir.upm.edu.my/id/eprint/40617/
http://www.pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2022%20%282%29%20Jul.%202014/03%20JST%200376%202012.pdf
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spelling my.upm.eprints.406172015-11-27T01:03:12Z http://psasir.upm.edu.my/id/eprint/40617/ Hypothesis tests of goodness-of-fit for Fréchet distribution Zainal Abidin, Nahdiya Adam, Mohd Bakri Midi, Habshah Extreme Value Theory (EVT) is a statistical field whose main focus is to investigate extreme phenomena. In EVT, Fréchet distribution is one of the extreme value distributions and it is used to model extreme events. The degree of fit between the model and the observed values was measured by Goodness-of-fit (GOF) test. Several types of GOF tests were also compared. The tests involved were Anderson-Darling (AD), Cramer-von Mises (CVM), Zhang Anderson Darling (ZAD), Zhang Cramer von-Mises (ZCVM) and Ln. The values of parameters μ, σ and ξ were estimated by Maximum Likelihood. The critical values were developed by Monte-Carlo simulation. In power study, the reliability of critical values was determined. Besides, it is of interest to identify which GOF test is superior to the other tests for Fréchet distribution. Thus, the comparisons of rejection rates were observed at different significance levels, as well as different sample sizes, based on several alternative distributions. Overall, given by Maximum Likelihood Estimation of Fréchet distribution, the ZAD and ZCVM tests are the most powerful tests for smaller sample size (ZAD for significance levels 0.05 and 0.1, ZCVM for significance level 0.01) as compared to AD, which is more powerful for larger sample size. Universiti Putra Malaysia Press 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/40617/1/100.%20Hypothesis%20Tests%20of%20Goodness-of-Fit%20for%20Fr%C3%A9chet%20Distribution.pdf Zainal Abidin, Nahdiya and Adam, Mohd Bakri and Midi, Habshah (2014) Hypothesis tests of goodness-of-fit for Fréchet distribution. Pertanika Journal of Science & Technology, 22 (2). pp. 419-432. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2022%20%282%29%20Jul.%202014/03%20JST%200376%202012.pdf
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Extreme Value Theory (EVT) is a statistical field whose main focus is to investigate extreme phenomena. In EVT, Fréchet distribution is one of the extreme value distributions and it is used to model extreme events. The degree of fit between the model and the observed values was measured by Goodness-of-fit (GOF) test. Several types of GOF tests were also compared. The tests involved were Anderson-Darling (AD), Cramer-von Mises (CVM), Zhang Anderson Darling (ZAD), Zhang Cramer von-Mises (ZCVM) and Ln. The values of parameters μ, σ and ξ were estimated by Maximum Likelihood. The critical values were developed by Monte-Carlo simulation. In power study, the reliability of critical values was determined. Besides, it is of interest to identify which GOF test is superior to the other tests for Fréchet distribution. Thus, the comparisons of rejection rates were observed at different significance levels, as well as different sample sizes, based on several alternative distributions. Overall, given by Maximum Likelihood Estimation of Fréchet distribution, the ZAD and ZCVM tests are the most powerful tests for smaller sample size (ZAD for significance levels 0.05 and 0.1, ZCVM for significance level 0.01) as compared to AD, which is more powerful for larger sample size.
format Article
author Zainal Abidin, Nahdiya
Adam, Mohd Bakri
Midi, Habshah
spellingShingle Zainal Abidin, Nahdiya
Adam, Mohd Bakri
Midi, Habshah
Hypothesis tests of goodness-of-fit for Fréchet distribution
author_facet Zainal Abidin, Nahdiya
Adam, Mohd Bakri
Midi, Habshah
author_sort Zainal Abidin, Nahdiya
title Hypothesis tests of goodness-of-fit for Fréchet distribution
title_short Hypothesis tests of goodness-of-fit for Fréchet distribution
title_full Hypothesis tests of goodness-of-fit for Fréchet distribution
title_fullStr Hypothesis tests of goodness-of-fit for Fréchet distribution
title_full_unstemmed Hypothesis tests of goodness-of-fit for Fréchet distribution
title_sort hypothesis tests of goodness-of-fit for fréchet distribution
publisher Universiti Putra Malaysia Press
publishDate 2014
url http://psasir.upm.edu.my/id/eprint/40617/1/100.%20Hypothesis%20Tests%20of%20Goodness-of-Fit%20for%20Fr%C3%A9chet%20Distribution.pdf
http://psasir.upm.edu.my/id/eprint/40617/
http://www.pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2022%20%282%29%20Jul.%202014/03%20JST%200376%202012.pdf
_version_ 1643832767957434368
score 13.211869

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