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Generalized Gumbel distribution

Author

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  • Kahadawala Cooray

Abstract

A generalization of the Gumbel distribution is presented to deal with general situations in modeling univariate data with broad range of skewness in the density function. This generalization is derived by considering a logarithmic transformation of an odd Weibull random variable. As a result, the generalized Gumbel distribution is not only useful for testing goodness-of-fit of Gumbel and reverse-Gumbel distributions as submodels, but it is also convenient for modeling and fitting a wide variety of data sets that are not possible to be modeled by well-known distributions. Skewness and kurtosis shapes of the generalized Gumbel distribution are illustrated by constructing the Galton's skewness and Moor's kurtosis plane. Parameters are estimated by using maximum likelihood method in two different ways due to the fact that the reverse transformation of the proposed distribution does not change its density function. In order to illustrate the flexibility of this generalization, wave and surge height data set is analyzed, and the fitness is compared with Gumbel and generalized extreme value distributions.

Suggested Citation

  • Kahadawala Cooray, 2010. "Generalized Gumbel distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 171-179.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:1:p:171-179
    DOI: 10.1080/02664760802698995
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    Cited by:

    1. Louis Geiler & Séverine Affeldt & Mohamed Nadif, 2022. "A survey on machine learning methods for churn prediction," Post-Print hal-03824873, HAL.
    2. Wilson Gyasi & Kahadawala Cooray, 2024. "New generalized extreme value distribution with applications to extreme temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    3. Sun, Huiqian & Jing, Peng & Wang, Baihui & Cai, Yunhao & Ye, Jie & Wang, Bichen, 2023. "The effect of record-high gasoline prices on the consumers’ new energy vehicle purchase intention: Evidence from the uniform experimental design," Energy Policy, Elsevier, vol. 175(C).
    4. Qingyang Liu & Xianzheng Huang & Haiming Zhou, 2024. "The Flexible Gumbel Distribution: A New Model for Inference about the Mode," Stats, MDPI, vol. 7(1), pages 1-16, March.
    5. Mohammad A. Aljarrah & Felix Famoye & Carl Lee, 2020. "Generalized logistic distribution and its regression model," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-21, December.

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