The Flexible Fréchet Distribution: Properties, Inference, and Medical Applications

Abstract

This paper introduces the Marshall–Olkin Weibull–Fréchet (MOWFr) distribution, a modified form of the Fréchet model that demonstrates improved fitting capabilities compared to established generalizations. We present key properties of the MOWFr distribution, noting that its density function can be symmetric, right-skewed, or unimodal. The failure rate can exhibit monotonically increasing, J-shaped, and modified bathtub patterns, making it a flexible tool for analyzing real-life data across various fields. We briefly describe several frequentist approaches for estimating the MOWFr parameters and evaluate their performance through simulation studies, ranked by partial and overall effectiveness for small and large samples. The results indicate that maximum likelihood estimation is the most effective method for parameter estimation. Finally, we illustrate the practical applicability of the MOWFr distribution by modeling two real-life medical datasets.