Authors: Margret Igiozee, Jimoh M. Afolabi and Ehigie, O. Timothy

Citation: Margret Igiozee, Jimoh M. Afolabi and Ehigie, O. Timothy (2025). On development of exponentiated frechet weibull distribution: properties and applications. Frontline Professionals Journal 2(5), 35-46

The Exponentiated Fréchet-Weibull (EF-Weibull) distribution is introduced as a flexible statistical model that extends the classical Fréchet and Weibull distributions by incorporating additional shape and scale parameters. This study derives its probability density function (PDF), cumulative distribution function (CDF), quantile function, hazard function, and moment-based properties, providing a comprehensive theoretical foundation. Maximum likelihood estimation (MLE) was employed for parameter estimation, ensuring its applicability to real-world datasets. A comparative analysis was conducted against the Exponentiated Fréchet (Exp-Fréchet), Exponentiated Weibull (Exp-Weibull), Exponentiated Exponential (Exp-Exponential), Fréchet, and Weibull distributions using log-likelihood (LL), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov (KS) test, Anderson-Darling (AD) test, and Cramér-von Mises (CS) test. The results showed that the EF-Weibull distribution provided the best fit, achieving the highest LL and lowest AIC and BIC values, while also demonstrating superior empirical performance through KS, AD, and CS test statistics. Graphical evaluations, including histogram density plots, hazard function plots, and empirical CDF comparisons, further validated its modeling efficiency. The study concludes that the EF-Weibull distribution is an effective model for reliability analysis, survival analysis, and extreme value modeling.

Keywords: Exponentiated, Fréchet-Weibull, distribution, Applications, Distribution