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

Published in International Journal of Statistical Distributions and Applications (Volume 1, Issue 1)

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.

Published in	International Journal of Statistical Distributions and Applications (Volume 1, Issue 1)
DOI	10.11648/j.ijsd.20150101.14
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), 2015. 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
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N1  - https://doi.org/10.11648/j.ijsd.20150101.14
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JO  - International Journal of Statistical Distributions and Applications
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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
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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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