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A COMPREHENSIVE REVIEW OF TRANSMUTED DISTRIBUTIONS

AUTHORS:
Nandini N Golekar
Mentor
Affiliation
Department of Statistics Punyashlok Ahilyadevi Holkar Solapur University, Solapur (MS), India-413255
CC BY 4.0 License:
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract

In recent years, the development of flexible statistical distributions has gained considerable attention due to the increasing complexity of real-world data. Among various generalization techniques, the transmuted family of distributions has emerged as an effective and mathematically tractable approach for enhancing classical distributions. This family is generated using the quadratic rank transmutation map (QRTM), which introduces an additional parameter to control skewness and kurtosis. The present paper provides a comprehensive review of transmuted distributions, discussing their theoretical foundation, historical development, major contributions, and applications. The study also classifies the existing literature and identifies potential areas for future research.

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Golekar, N. N. (2026). A Comprehensive Review of Transmuted Distributions. International Journal of Science, Strategic Management and Technology, 02(04). https://doi.org/10.55041/ijsmt.v2i4.054

Golekar, Nandini. "A Comprehensive Review of Transmuted Distributions." International Journal of Science, Strategic Management and Technology, vol. 02, no. 04, 2026, pp. . doi:https://doi.org/10.55041/ijsmt.v2i4.054.

Golekar, Nandini. "A Comprehensive Review of Transmuted Distributions." International Journal of Science, Strategic Management and Technology 02, no. 04 (2026). https://doi.org/https://doi.org/10.55041/ijsmt.v2i4.054.

References
1.Afify, A. Z., Nofal, Z. M., & Ebraheim, A. N. (2015). Transmuted Marshall–Olkin Fréchet distribution: Properties and applications. International Journal of Statistics and Probability, 4(4), 132–148. https://doi.org/10.5539/ijsp.v4n4p132

2.Aryal, G. R., & Tsokos, C. P. (2011). Transmuted Weibull distribution: A generalization of the Weibull probability distribution. European Journal of Pure and Applied Mathematics, 4(2), 89– 102.

3.Ashour, S. K., & Eltehiwy, M. A. (2013). Transmuted Lomax distribution. American Journal of Applied Mathematics and Statistics, 1(6), 121–127. https://doi.org/10.12691/ajams-1-6-3

4.Elbatal, I. (2013). Transmuted inverse Weibull distribution. Journal of Statistics Applications & Probability, 2(2), 149–160.

5.Khan, M. S., & King, R. (2013). Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. European Journal of Pure and Applied Mathematics, 6(1), 66–88.

6.Merovci, F. (2013). Transmuted Rayleigh distribution. Austrian Journal of Statistics, 42(1), 21– 31.

7.Nofal, Z. M., Afify, A. Z., Yousof, H. M., & Cordeiro, G. M. (2017). The exponentiated transmuted-G family of distributions. Communications in Statistics – Theory and Methods, 46(10), 5407–5428. https://doi.org/10.1080/03610926.2015.1096354

8.Oguntunde, P. E., & Adejumo, A. O. (2015). The transmuted exponential distribution: Properties and applications. SpringerPlus, 4, 1–8. https://doi.org/10.1186/s40064-015-1590-6

9.Shaw, W. T., & Buckley, I. R. C. (2007). The alchemy of probability distributions: Beyond Gram–Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report.

10.Silva, R. P. D., Percontini, A., de Brito, E., Ramos, M. W. A., Venancio, R., & Cordeiro, G. M. (2020). The transmuted Marshall–Olkin extended Lomax distribution. Journal of King Saud University – Science, 32(1), 548–557. https://doi.org/10.1016/j.jksus.2018.05.006
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This article has undergone plagiarism screening and double-blind peer review. Editorial policies have been followed. Authors retain copyright under CC BY-NC 4.0 license. The research complies with ethical standards and institutional guidelines.
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