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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science
Full Length Article

Volume 23 • Issue 3 • PP: 229-236 • 2024

A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data

Hanaa Saad M. Shibeeb 1*
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,
S. Altalaqani 1
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,
A. AL-Adilee 2
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1Department of Economy, Faculty of Management and Economy, University of Kufa, Iraq
2Department of Mathematics, Faculty of Education, University of Kufa, Iraq
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.230327
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: August 13, 2023 Revised: December 12, 2023 Accepted: February 25, 2024
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Abstract

In this paper, we propose a new version of the Gumbel Distribution using a sine technique family. We discuss the key properties of this distribution, such as the probability density function, the cumulative distribution function, the survival function, the hazard function, the cumulative hazard, and the moments. Additionally, we present a method for estimating the distribution's parameters. We then analyze a dataset using the original and generalized distributions, comparing the results and using goodness-of-fit measures to determine which distribution best fits the data. Finally, we provide conclusions based on our findings, with many examples and valid comparisons applied on fuzzy data.

Keywords

Continues Distributions Statistical Properties Gumbel distribution Trigonometric Functions Estimations Methods Statistical Inference fuzzy data fuzzy analysis.

References

[1]  Cooray, Kahadawala. "Generalized gumbel distribution." Journal of Applied Statistics 37.1 (2010): 171-179.

[2]  Nadarajah, Saralees, and Samuel Kotz. "The beta Gumbel distribution." Mathematical Problems in engineering 2004 (2004): 323-332.

[3]  Andrade, Thiago, et al. "The exponentiated generalized Gumbel distribution." Revista Colombiana de Estadística 38.1 (2015): 123-143.

[4]  Ghitany, M. E., E. K. Al-Hussaini, and R. A. Al-Jarallah. "Marshall–Olkin extended Weibull distribution and its application to censored data." Journal of Applied Statistics 32.10 (2005): 1025-1034.

[5]  Ishaq, Aliyu Ismail, and Alfred Adewole Abiodun. "The Maxwell–Weibull distribution in modeling lifetime datasets." Annals of Data Science 7.4 (2020): 639-662.

[6]  Ahmed, AL-Adilee, et al. "GENERALIZED LINDLEY DISTRIBUTION USING PROPORTIONAL HAZARD FAMILY AND INFERENCE OF FAILURE TIME DATA." Nonlinear Functional Analysis and Applications (2023): 793-800.

[7]  Marshall, Albert W., and Ingram Olkin. "A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families." Biometrika 84.3 (1997): 641-652.

[8]  Kumar, Dinesh, Umesh Singh, and Sanjay Kumar Singh. "A new distribution using sine function-its application to bladder cancer patients data." Journal of Statistics Applications & Probability 4.3 (2015): 417.

[9]  Chesneau, Christophe, and Farrukh Jamal. "The sine Kumaraswamy-G family of distributions." Journal of Mathematical Extension 15 (2020).

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Shibeeb, Hanaa Saad M., Altalaqani, S., AL-Adilee, A.. "A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, 2024, pp. 229-236. DOI: https://doi.org/10.54216/IJNS.230327
Shibeeb, H., Altalaqani, S., AL-Adilee, A. (2024). A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data. International Journal of Neutrosophic Science, Volume 23(Issue 3), 229-236. DOI: https://doi.org/10.54216/IJNS.230327
Shibeeb, Hanaa Saad M., Altalaqani, S., AL-Adilee, A.. "A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data." International Journal of Neutrosophic Science Volume 23, no. Issue 3 (2024): 229-236. DOI: https://doi.org/10.54216/IJNS.230327
Shibeeb, H., Altalaqani, S., AL-Adilee, A. (2024) 'A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data', International Journal of Neutrosophic Science, Volume 23(Issue 3), pp. 229-236. DOI: https://doi.org/10.54216/IJNS.230327
Shibeeb H, Altalaqani S, AL-Adilee A. A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 3):229-236. DOI: https://doi.org/10.54216/IJNS.230327
H. Shibeeb, S. Altalaqani, A. AL-Adilee, "A New Version of Gumbel Distribution Using Sine Technique Family: Properties, Parameter Estimation, and Data Analysis and Comparison with Fuzzy Data," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 3, pp. 229-236, 2024. DOI: https://doi.org/10.54216/IJNS.230327
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