Exploring the Statistical Treatments, Different Methods of Parameter Estimation, and Practical Applications of a New Probability Model

  • Thomas Ejemah Department of Statistics, Southern Delta University, Ozoro, Nigeria
  • Francis E. Itiveh Department of Statistics, Southern Delta University, Ozoro, Nigeria
  • Godspower A. Eriyeva Department of Statistics, Southern Delta University, Ozoro, Nigeria
  • Efezino P. Omosioni Department of Statistics, Southern Delta University, Ozoro, Nigeria
  • Festus C. Opone Department of Statistics, Southern Delta University, Ozoro, Nigeria
DOI: https://doi.org/10.34198/ejms.15525.755778
Keywords: Fréchet distribution, MTI transformation, methods of parameter estimation, quantiles

Abstract

This paper proposes a new three-parameter generalized Fréchet distribution using the MTI transformation scheme. We refer to the proposed model as MTI-Fréchet (MTIF) distribution. Several statistical treatments of the MTIF distribution, including survival, hazard rate, and quantile functions, moments, incomplete moments, moment-generating function, probability-weighted moment, and Renyi entropy, are derived. The study adopts four methods of parameter estimation to estimate the parameters of the MTIF distribution, followed by a simulation experiment to investigate the performance of the parameter estimates based on the four methods. The simulation results suggest that the MPS is the most appropriate estimation method for estimating the parameters of the MTIF distribution. The flexibility of the proposed MTIF distribution in practical data fitting is illustrated using two data sets. The results obtained from some model selection criteria and goodness-of-fit test statistics revealed that the MTIF distribution offered a better fit for the data sets compared to the classical Fréchet distribution and other generalized Fréchet distributions.

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Published
2025-06-23
How to Cite
Ejemah, T., Itiveh, F. E., Eriyeva, G. A., Omosioni, E. P., & Opone, F. C. (2025). Exploring the Statistical Treatments, Different Methods of Parameter Estimation, and Practical Applications of a New Probability Model. Earthline Journal of Mathematical Sciences, 15(5), 755-778. https://doi.org/10.34198/ejms.15525.755778
Issue
Vol 15 No 5 (2025): In progress
Section
Articles


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