Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data

Mustafa Ç. Korkmaz

doi:doi:10.11648/j.ijsd.20150101.14

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Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data

Mustafa Ç. Korkmaz

Received: 21 September 2015 Accepted: 6 October 2015 Published: 14 October 2015

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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.

DOI	10.11648/j.ijsd.20150101.14
Published in	International Journal of Statistical Distributions and Applications (Volume 1, Issue 1, September 2015)
Page(s)	19-26
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Gumbel Distribution, Two-Sided Distribution, Generalized Gumbel Distribution, Exponentiated Gumbel Distribution

References

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[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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Mustafa Ç. Korkmaz. (2015). Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data. International Journal of Statistical Distributions and Applications, 1(1), 19-26. https://doi.org/10.11648/j.ijsd.20150101.14

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ACS Style

Mustafa Ç. Korkmaz. Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data. Int. J. Stat. Distrib. Appl. 2015, 1(1), 19-26. doi: 10.11648/j.ijsd.20150101.14

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AMA Style

Mustafa Ç. Korkmaz. Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data. Int J Stat Distrib Appl. 2015;1(1):19-26. doi: 10.11648/j.ijsd.20150101.14

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@article{10.11648/j.ijsd.20150101.14,
  author = {Mustafa Ç. Korkmaz},
  title = {Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {1},
  number = {1},
  pages = {19-26},
  doi = {10.11648/j.ijsd.20150101.14},
  url = {https://doi.org/10.11648/j.ijsd.20150101.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20150101.14},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data
AU  - Mustafa Ç. Korkmaz
Y1  - 2015/10/14
PY  - 2015
N1  - https://doi.org/10.11648/j.ijsd.20150101.14
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JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
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EP  - 26
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SN  - 2472-3509
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AB  - 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.
VL  - 1
IS  - 1
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Mustafa Ç. Korkmaz

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APA Style

Mustafa Ç. Korkmaz. (2015). Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data. International Journal of Statistical Distributions and Applications, 1(1), 19-26. https://doi.org/10.11648/j.ijsd.20150101.14

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ACS Style

Mustafa Ç. Korkmaz. Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data. Int. J. Stat. Distrib. Appl. 2015, 1(1), 19-26. doi: 10.11648/j.ijsd.20150101.14

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AMA Style

Mustafa Ç. Korkmaz. Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data. Int J Stat Distrib Appl. 2015;1(1):19-26. doi: 10.11648/j.ijsd.20150101.14

Copy | Download

@article{10.11648/j.ijsd.20150101.14,
  author = {Mustafa Ç. Korkmaz},
  title = {Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {1},
  number = {1},
  pages = {19-26},
  doi = {10.11648/j.ijsd.20150101.14},
  url = {https://doi.org/10.11648/j.ijsd.20150101.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20150101.14},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Two-Sided Generalized Gumbel Distribution with Application to Air Pollution Data
AU  - Mustafa Ç. Korkmaz
Y1  - 2015/10/14
PY  - 2015
N1  - https://doi.org/10.11648/j.ijsd.20150101.14
DO  - 10.11648/j.ijsd.20150101.14
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 19
EP  - 26
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20150101.14
AB  - 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.
VL  - 1
IS  - 1
ER  -

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