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

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.