The Cubic Rank Transmuted Gumbel Distribution
DOI:
https://doi.org/10.29304/jqcm.2023.15.1.1183Keywords:
Cubic rank transmuted, Gumbel Distribution, Renyi Entropy, Shannon EntropyAbstract
A Cubic Rank Transmuted Gumbel distribution (CTGD) in this research is extend the work of cubic transmuted distribution families. CTGD improves the flexibility of transmuted distributions and allows for the modeling of more complex data. Its hazard rate function, moment-generating function, moments, quantile function, entropy and order statistics, are only a few of the key statistical characteristics that we examine. Finally, the Cubic Transmuted Gumbel Distribution is applied to three real datasets to test its applicability and evaluate how well estimate approaches function for the CTGD, Gumbel(G), and transmuted Gumbel (TG) distributions. The observed results demonstrated that, for the used data sets, CTGD provides a superior fit than G and TG distributions.
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References
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[2] S. Arifa, M. Z. Yab, and A. Ali, "The modified burr iii g family of distributions". Journal of Data Science, (2017), 15(1):41–60.
[3] G. R. Aryal, and C. P. Tsokos, "On the transmuted extreme value distribution with application". Nonlinear Analysis: Theory, Methods and Applications, (2009), 71:e1401–e1407.
[4] F. Proschan , " Theoretical Explanation of Observed Decreasing Failure Rate ", Technometrics, (1963).
, Brazilian Journal of Probability and Statistics, (2012), 26, 88-112.
[5] G. Casella, and R. L. Berger, "Statistical inference", Cengage Learning, (2021).
[6] D.Deka, B. Das, and B. K. Baruah, "Transmuted exponentiated gumbel distribution (tegd) and its application to water quality data", Pakistan Journal of Statistics and Operation Research, (2017), pp. 115–126.
[7] D. C. T. Granzotto, F. Louzada, N. and Balakrishnan, "Cubic rank transmuted distributions: inferential issues and applications", Journal of statistical Computation and Simulation, (2017), 87:2760–2778.
[8] . E. J. Gumbel, "Les valeurs extremes des distributions statistiques",Annales de l'institut Henri Poincaré, (1935), V. 5, pp. 115–158.
[9] J. Havrda, and F. Charvat, "Quantification method of classification processes. concept of structural a-entropy", Kybernetika, (1967), 3(1):30–35.
[10] S. Kotz, and S. Nadarajah, "Extreme value distributions: theory and applications", World Scientific,(2000).
[11] E. T. Lee, and J. Wang, "Statistical methods for survival data analysis", John Wiley & Sons,(2003), v. 476.
[12] S. Nadarajah, "The exponentiated gumbel distribution with climate application. Environmetrics",The official journal of the International Environmetrics Society, (2006), 17:13–23.
[13] S. Nadarajah, and S. Kotz, "The beta gumbel distribution", Mathematical Problems in engineering, (2004), pp.323–332.
[14] I. E. Okorie, A. C. Akpanta, and J. Ohakwe, "The exponentiated gumbel type-2 distribution: properties and application", International Journal of Mathematics and Mathematical Sciences, (2016).
[15] M. M. Rahman, B. Al-Zahrani, and M. Q. Shahbaz, "A general transmuted family of distributions", Pakistan Journal of Statistics and Operation Research, (2018), pp. 451–469.
[16] A. Renyi, et al. "On measures of information and entropy", In Proceedings of the 4th Berkeley symposium on mathematics, statistics and probability, (1961), v. 1.
[17] C. E. Shannon, "A mathematical theory of communication", The Bell system technical journal, (1948), 27(3):379–423.
[18] W. T Shaw,. and I. R. C. Buckley, "The alchemy of probability distributions: beyond gramcharlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map", arXiv, (2009),0901.0434.
[19] F. Merovci, and, L. Puka, "Transmuted Pareto Distribution". Probstat Forum, (2014), 7: 1-11.
[20] A. Ullah, "Entropy, divergence and distance measures with econometric applications", Journal of Statistical Planning and Inference, (1996), 49(1):137–162.
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Published
2023-04-07
How to Cite
ELHertaniy, D. A., & Bashir Hamid, A. R. (2023). The Cubic Rank Transmuted Gumbel Distribution. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(1), Stat. Page 1–18. https://doi.org/10.29304/jqcm.2023.15.1.1183
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Statistic Articles
