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Hybrid conditional plot of goodness-of-fit for Gumbel distribution

A Gumbel model is an extreme value model that describes the event of extreme behaviour. The Gumbel model has an exponential tail. Generally, the goodness-of-fit for the Gumbel model is evaluated by the graphical form of probability plot (PP) and quantiles plot (QQ). The model fits the observed value...

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Main Authors: Zainal Abidin, Nahdiya, Adam, Mohd Bakri, Midi, Habshah
Format: Article
Language:English
Published: Universiti Kebangsaan Malaysia 2012
Online Access:http://psasir.upm.edu.my/id/eprint/51849/1/Hybrid%20conditional%20plot%20of%20goodness-of-fit%20for%20Gumbel%20distribution.pdf
http://psasir.upm.edu.my/id/eprint/51849/
http://www.ukm.my/jqma/jqma8_1a.html
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spelling my.upm.eprints.518492017-05-02T08:05:05Z http://psasir.upm.edu.my/id/eprint/51849/ Hybrid conditional plot of goodness-of-fit for Gumbel distribution Zainal Abidin, Nahdiya Adam, Mohd Bakri Midi, Habshah A Gumbel model is an extreme value model that describes the event of extreme behaviour. The Gumbel model has an exponential tail. Generally, the goodness-of-fit for the Gumbel model is evaluated by the graphical form of probability plot (PP) and quantiles plot (QQ). The model fits the observed values if the probability and the quantiles of the hypothetical distribution are linearly plotted against that of the observed values. However, the QQ plot is quite sensitive to the deviation at the tail of the plot, as opposed to the PP plot which is somewhat robust. Thus, distribution of extreme values is likely to deviate from the linear line at the tail of the QQ plot. An alternative approach of plotting the Gumbel model is given, in which the approach is expected to produce the linear plot. The conditional plot and stabilised plot are employed and the performances of both are compared. The plots are transformed into the hybrid plot so that the departures of the hypothetical quantiles values from the observed quantiles values are illustrated. The result shows that the hybrid conditional QQ plot is a better plot of goodness-of-fit for Gumbel model. Universiti Kebangsaan Malaysia 2012 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51849/1/Hybrid%20conditional%20plot%20of%20goodness-of-fit%20for%20Gumbel%20distribution.pdf Zainal Abidin, Nahdiya and Adam, Mohd Bakri and Midi, Habshah (2012) Hybrid conditional plot of goodness-of-fit for Gumbel distribution. Journal of Quality Measurement and Analysis, 8 (1). pp. 43-53. ISSN 1823-5670 http://www.ukm.my/jqma/jqma8_1a.html
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 A Gumbel model is an extreme value model that describes the event of extreme behaviour. The Gumbel model has an exponential tail. Generally, the goodness-of-fit for the Gumbel model is evaluated by the graphical form of probability plot (PP) and quantiles plot (QQ). The model fits the observed values if the probability and the quantiles of the hypothetical distribution are linearly plotted against that of the observed values. However, the QQ plot is quite sensitive to the deviation at the tail of the plot, as opposed to the PP plot which is somewhat robust. Thus, distribution of extreme values is likely to deviate from the linear line at the tail of the QQ plot. An alternative approach of plotting the Gumbel model is given, in which the approach is expected to produce the linear plot. The conditional plot and stabilised plot are employed and the performances of both are compared. The plots are transformed into the hybrid plot so that the departures of the hypothetical quantiles values from the observed quantiles values are illustrated. The result shows that the hybrid conditional QQ plot is a better plot of goodness-of-fit for Gumbel model.
format Article
author Zainal Abidin, Nahdiya
Adam, Mohd Bakri
Midi, Habshah
spellingShingle Zainal Abidin, Nahdiya
Adam, Mohd Bakri
Midi, Habshah
Hybrid conditional plot of goodness-of-fit for Gumbel distribution
author_facet Zainal Abidin, Nahdiya
Adam, Mohd Bakri
Midi, Habshah
author_sort Zainal Abidin, Nahdiya
title Hybrid conditional plot of goodness-of-fit for Gumbel distribution
title_short Hybrid conditional plot of goodness-of-fit for Gumbel distribution
title_full Hybrid conditional plot of goodness-of-fit for Gumbel distribution
title_fullStr Hybrid conditional plot of goodness-of-fit for Gumbel distribution
title_full_unstemmed Hybrid conditional plot of goodness-of-fit for Gumbel distribution
title_sort hybrid conditional plot of goodness-of-fit for gumbel distribution
publisher Universiti Kebangsaan Malaysia
publishDate 2012
url http://psasir.upm.edu.my/id/eprint/51849/1/Hybrid%20conditional%20plot%20of%20goodness-of-fit%20for%20Gumbel%20distribution.pdf
http://psasir.upm.edu.my/id/eprint/51849/
http://www.ukm.my/jqma/jqma8_1a.html
_version_ 1643835074035056640
score 13.211869

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