In this paper, a new four-parameter exponential-transmuted exponential (ETE) distribution is proposed based on the T-X transformation method, which extends and improves the existing ETE distribution by introducing an additional shape parameter. Several important properties of the new distribution are systematically explored in the paper, including the construction of moments, mother-of-moment function and risk function. In order to verify the applicability of the new distribution in real data, the paper uses the great likelihood estimation method to fit the new distribution to the payout data with heavy-tailed characteristics in the U.S. compensation loss dataset. By comparing with the classical models such as the original three-parameter ETE distribution, the Weibull exponential (WE) distribution and the exponential (E) distribution, the results show that the newly proposed ETE distribution outperforms other models in terms of fitting effect and information criterion, which further validates its robustness and applicability in complex data processing.

Bin Han. The Four-Parameter Exponential-Transmuted Exponential Distribution: Properties and Applications. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 3: 82-90. https://doi.org/10.25236/AJMS.2024.050312.

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