A New Version of Cubic Rank Transmuted Gumbel Distribution | ||
Kirkuk Journal of Science | ||
Article 1, Volume 18, Issue 1, March 2023, Pages 1-15 PDF (813.08 K) | ||
Document Type: Research Paper | ||
DOI: 10.32894/kujss.2023.136740.1084 | ||
Author | ||
Doaa Abd K. Elhertaniy* | ||
Department of Mathematics, university of the Holy Quran and Taseel of Science, Sudan. | ||
Abstract | ||
A Cubic Rank Transmuted Gumbel distribution (CTGD) in this article is a new generalization of the Gumbel distribution based on a cubic ranking transmutation map. Examined are the cubic transmuted Gumbel model's fundamental statistical properties, such as its hazard rate function, moment-generating function, moments, characteristic function, quantile function, entropy, and order statistics. Finally, the usefulness and applicability of the CTGD using two real data sets about waiting time at a bank is described and Wheaton River flood, and the fit has been compared with Gumbel distribution (GD) and transmuted Gumbel distribution (TGD). The results show that the proposed model provides a superior fit than transmuted Gumbel distributions and Gumbel distributions. | ||
Keywords | ||
Moments; Gumbel Distribution; simulation study; order statistics; Entropy | ||
References | ||
[1]Les valeurs extremes des distributions statistiques. Annales de l’institut Henri Poincar ́e, 5(2), 1935.
[2]Kotz Samuel and Nadarajah Saralees. Extreme value distributions: theory and applications. world scientific, London, 2ededition, 2000. [3]SaraleesNadarajahandSamuelKotz.The betagumbeldistribution.Mathematical Problems in engineering,2004: 323–332,2004, doi:10.1155/S1024123X04403068. [4]Saralees Nadarajah. The exponentiated gumbel distribution with climate application. environmetrics.The official journal of the International Environmetrics Society, 17:13–23, 2006. [5]Idika E. Okorie, Anthony Akpanta, and J. Ohakwe. The exponentiated gumbel type-2 distribution:properties and application.International Journal of Mathematics and Mathematical Sciences, 2016(2): 1–10, 2016, doi:10.1155/2016/5898356. [6]S. Qurat ul Ain Ahmad Aijaz and Rajnee Tripathi. Transmuted gumbel type-ii distribution with applications in diverse fields of science.Pakistan Journal Statistics, 37: 429–446, 2021. [7]Deepshikha Deka, Bhanita Das, and Bhupen K. Baruah. Transmuted exponentiated gumbel distribution (tegd) and its application to water quality data.Pakistan Journal of Statistics and Operation Research, 13(1): 115–126, 2017, doi:10.18187/pjsor.v13i1.1636. [8]Gokarna R. Aryal and Chris P. Tsokos. On the transmuted extreme value distribution with application.Nonlinear Analysis, 71: e1401–e1407, 2009. [9]William T. Shaw and Ian RC. Buckley.he alchemy of probability distributions:beyond gramcharlier ex- pansions, and a skew-kurtotic-normal distribution from a rank transmutation map.arXiv:0901.0434, 2009, doi:10.48550/arXiv.0901.0434. [10]Bander Al-Zahran Md. Mahabubur Rahman, Saman H Shahbaz,and Muhammad Qaiser Shahbaz.Cubic transmuted uniform distribution: An alternative to beta and kumaraswamy distributions.European Journal of Pure and Applied Mathematics, 12: 1106–1121, 2019, doi:10.29020/nybg.ejpam.v12i3.3410. [11]Zhongfeng Sun and Huizeng Qin. Some results on the derivatives of the gamma and incomplete gamma function for non-positive integers.IAENG International Journal of Applied Mathematics, 47(3): 265–270, 2017. [12]Alfr ́ed R ́enyi. On measures of entropy and information. In Proceedings of the4thBerkeley symposium on mathematics, statistics and probability, 1: 547–561, 1961. [13]Jan Havrda and Frantiˇsek Charv ́at. Quantification method of classification processes. concept of structural a-entropy. Kybernetika, 3(1): 30–35, 1967. [14]Aman Ullah.Entropy, divergence and distance measures with econometric applications.Journal of Statistical Planning and Inference, 49(1): 137–162, 1996, doi:10.1016/0378-3758(95)00034-8. [15]Claude E. Shannon. A mathematical theory of communication.The Bell system technical journal, 27(3): 379–423, 1948, doi:10.1002/j.1538-7305.1948.tb00917.x. [16]G. Casella and L. Berger.Statistical inference. CengageLearning, USA, 2ededition, 2021. [17]Mohamed E.Ghitany, Atieh Barbra, and Saralees Nadarajah.Lindley distribution and its application, math- ematics and computers in simulation.Mathematics and computers in simulation, 78: 493–506, 2008, doi:10.1016/j.matcom.2007.06.007. [18]Faton Merovci and Lukan Puka. Transmuted pareto distribution.ProbStat Forum, 7(1): 1–11, 2014. Kirkuk U. J. Sci. Stud. Vol. 18, Iss. 1, p 00-00, 2023 | ||
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