Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data
International Journal of Statistical Distributions and Applications
Volume 1, Issue 1, September 2015, Pages: 19-26
Received: Sep. 21, 2015; Accepted: Oct. 6, 2015; Published: Oct. 14, 2015
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Author
Mustafa Ç. Korkmaz, ArtvinÇoruh University, Department of Statistics and Computer Sciences, Artvin/TURKEY
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Abstract
We introduce a univariate generalized form of the Gumbel distribution via two-sided distribution structure. We obtain its some properties such as special cases, density shapes, hazard rate function and moments. We give the maximum likelihood estimators of this two-sided generalized Gumbel distribution with an algorithm. Finally, a real data application based on air pollution data is given to demonstrate that it has real data modeling potential.
Keywords
Gumbel Distribution, Two-Sided Distribution, Generalized Gumbel Distribution, Exponentiated Gumbel Distribution
To cite this article
Mustafa Ç. Korkmaz, Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data, International Journal of Statistical Distributions and Applications. Vol. 1, No. 1, 2015, pp. 19-26. doi: 10.11648/j.ijsd.20150101.14
Copyright
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Al-Aqtash, R., Lee, C., Famoye, C. (2014). Gumbel-Weibull distribution: Properties and Applications. Journal of Modern Applied Statistical Methods, 13(2), 201-225.
[2]
Andrade, T., Rodrigues, H., Bourguignon, M., Cordeiro, G.M. (2015). The exponentiated generalized Gumbel Distribution. RevistaColombiana de Estadistica, 38(1), 123-143.
[3]
Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J. (2006). Statistics of Extremes: Theory and Applications. West Sussex, England: John Wiley and Sons Ltd.
[4]
Cooray, K. (2010). Generalized Gumbel distribution. Journal of Applied Statistics, 37(1), 171-179.
[5]
Cordeiro, G.M., Nadarajah, S., Ortega, E.M.M. (2012). The Kumaraswamy Gumbel distribution. Statistical Methods & Applications, 21, 139-168.
[6]
Cordeiro, G.M., Silva, G.O, Ortega, E.M.M. (2013). The beta-Weibull geometric distribution. Statistics: A Journal of Theoretical and Applied Statistics, 47(4), 817-834.
[7]
Gumbel, E.J. (1958). Statistics of Extremes, Columbia University Press, NewYork.
[8]
Johnson, N. L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions, Vol. 2 (2nd ed.). New York: John Wiley and Sons, Inc.
[9]
Korkmaz, M. Ç., Genç, A. I. (2014). A lifetime distribution based on a transformation of a two-Sided power variate. Journal of Statistical Theory and Applications, (in press).
[10]
Korkmaz, M.Ç., Genç, A.I., (2015). A New Generalized Two-sided Class of Distributions with an Emphasis on Two-sided Generalized Normal Distribution. Communications in Statistics Simulation and Computation, DOI: 10.1080/03610918.2015.1005233.
[11]
Kotz, S., Nadarajah, S. (2000). Extreme value distributions: theory and applications. Imperial College Press, London.
[12]
Leiva, V., Vilca, F., Balakrishnan, N., Sanhueza, A. (2010). A skewed sinh-normal distribution and its properties and application to air pollution. Communications in Statistics Theory and Methods, 39, 426-443.
[13]
Nadarajah, S. (2008). A truncated inverted beta distribution with application to air pollution data. Stochastic Environmental Research and Risk Assessment, 22, 285-289.
[14]
Nadarajah , S. (2006). The exponentiated Gumbel distribution with climate application. Environmetrics,17, 13-23.
[15]
Nadarajah, S., Kotz, S. (2004). The beta Gumbel Distribution. Mathematical Problems in Engineering, 4, 323–332.
[16]
Prudnikov, A. P., Brychkov, Y. A., Marichev, O. I. (1986). Integrals and series, vols 1, 2 and 3. Gordon and Breach Science Publishers, Amsterdam.
[17]
Van dorp, J. R., Kotz, S. (2002). The standard two-sided power distribution and itsproperties: With applications in financial engineering. The American Statistician, 56, 90–99.
[18]
Von Mises, R. (1954).La distribution de la grandede nvaleurs, American Mathematical Society, 271–294.
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