Fréchet Weibull Distribution: Properties and Application

Abstract

Recent advancements in distributional theory have increasingly focused on constructing flexible probability models capable of capturing complex real-world phenomena more effectively. Addressing this methodological need, this study introduces the Fréchet Weibull distribution, a novel extension of the classical Weibull model generated via the Fréchet-Generalized (Fr-G) family. This compound distribution exhibits enhanced skewness and structural versatility. We systematically derive its fundamental mathematical and statistical properties, alongside parameter estimation via the maximum likelihood method. The practical utility of the model is evaluated using a benchmark real-world dataset—specifically, the 10 mm gauge length data, and benchmarked against established counterparts, including the Lomax-Weibull, Weibull-Weibull, and Alpha Power Weibull distributions. Goodness-of-fit metrics, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC), demonstrate that the proposed model yields superior flexibility and empirical performance compared to existing alternatives.