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Comparative Analysis and Practical Applications of Cubic Transmutations for the Pareto Distribution

Author

Listed:
  • Edoh Katchekpele
  • Issa Cherif Geraldo
  • Tchilabalo Abozou Kpanzou

Abstract

Transmutation is a technique for extending classical probability distributions in order to give them more flexibility. In this paper, we are interested in cubic transmutations of the Pareto distribution. We establish a general formula that unifies the three existing cubic transmuted Pareto (CTP) distributions and facilitates the derivation of three new CTP distributions that have not yet been proposed in the literature. We also derive general formulas for the related mathematical properties and study parameter estimation via the maximum likelihood method. Finally, we perform a comparative analysis of the six CTP distributions using real‐world data. The results obtained confirm the flexibility and effectiveness of CTP distributions in modelling various types of data.

Suggested Citation

  • Edoh Katchekpele & Issa Cherif Geraldo & Tchilabalo Abozou Kpanzou, 2025. "Comparative Analysis and Practical Applications of Cubic Transmutations for the Pareto Distribution," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:1091306
    DOI: 10.1155/ijmm/1091306
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    1. Fathy H. Riad & Mohamed A. Sabry & Ehab M. Almetwally & Ramy Aldallal & Randa Alharbi & Md. Moyazzem Hossain & M. M. El-Dessoky, 2022. "On Extended Neoteric Ranked Set Sampling Plan: Likelihood Function Derivation and Parameter Estimation," Complexity, Hindawi, vol. 2022, pages 1-13, June.
    2. Edoh Katchekpele & Issa Cherif Geraldo & Tchilabalo Abozou Kpanzou, 2025. "Comparative Analysis and Practical Applications of Cubic Transmutations for the Pareto Distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-18, October.
    3. Fathy H. Riad & Mohamed A. Sabry & Ehab M. Almetwally & Ramy Aldallal & Randa Alharbi & Md. Moyazzem Hossain, 2022. "On Extended Neoteric Ranked Set Sampling Plan: Likelihood Function Derivation and Parameter Estimation," Complexity, John Wiley & Sons, vol. 2022(1).
    4. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    5. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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