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Gumbel distribution with heavy tails and applications to environmental data

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  • Gómez, Yolanda M.
  • Bolfarine, Heleno
  • Gómez, Héctor W.

Abstract

In this paper, we introduce a new extension to the extreme value type-1 (Gumbel) distribution, by constructing a slash type distribution. The result is a distribution with greater kurtosis than the Gumbel distribution. Properties of the distribution such as moments, moment generating function and kurtosis and asymmetry coefficients for the distribution are studied. Maximum likelihood estimation and moments estimators are applied and a simulation study is presented to illustrate parameter recovery. Results of applications to two real data sets, one from a wind velocity study and the other from snow accumulation indicate that the new model seems to perform better in the presence of atypical observations.

Suggested Citation

  • Gómez, Yolanda M. & Bolfarine, Heleno & Gómez, Héctor W., 2019. "Gumbel distribution with heavy tails and applications to environmental data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 115-129.
    • Handle: RePEc:eee:matcom:v:157:y:2019:i:c:p:115-129
    DOI: 10.1016/j.matcom.2018.10.003
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    References listed on IDEAS

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    1. Arslan, Olcay, 2008. "An alternative multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2756-2761, November.
    2. Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    3. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    4. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    5. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
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    Cited by:

    1. Nagode, Marko & Oman, Simon & Klemenc, Jernej & Panić, Branislav, 2023. "Gumbel mixture modelling for multiple failure data," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    2. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2022. "The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    3. Ziad M. Ali & Shady H. E. Abdel Aleem & Ahmed I. Omar & Bahaa Saad Mahmoud, 2022. "Economical-Environmental-Technical Operation of Power Networks with High Penetration of Renewable Energy Systems Using Multi-Objective Coronavirus Herd Immunity Algorithm," Mathematics, MDPI, vol. 10(7), pages 1-43, April.
    4. Juan M. Astorga & Jimmy Reyes & Karol I. Santoro & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Reliability Model Based on the Incomplete Generalized Integro-Exponential Function," Mathematics, MDPI, vol. 8(9), pages 1-12, September.
    5. Francisco A. Segovia & Yolanda M. Gómez & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Power Maxwell Distribution with Heavy Tails and Applications," Mathematics, MDPI, vol. 8(7), pages 1-20, July.
    6. Talha Arslan, 2021. "An α -Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    7. Ahmed I. Omar & Ziad M. Ali & Mostafa Al-Gabalawy & Shady H. E. Abdel Aleem & Mujahed Al-Dhaifallah, 2020. "Multi-Objective Environmental Economic Dispatch of an Electricity System Considering Integrated Natural Gas Units and Variable Renewable Energy Sources," Mathematics, MDPI, vol. 8(7), pages 1-37, July.
    8. Ruslan Abdulkadirov & Pavel Lyakhov & Nikolay Nagornov, 2022. "Accelerating Extreme Search of Multidimensional Functions Based on Natural Gradient Descent with Dirichlet Distributions," Mathematics, MDPI, vol. 10(19), pages 1-13, September.

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