Modeling Extreme Industrial Events under Indeterminacy Using Neutrosophic Fréchet Distribution

Fuad S. Alduais¹, Zahid Khan^2,*

¹Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia

²Department of Quantitative Methods, Pannon Egyetem, Veszprem, H-8200, Hungary

Emails f.alduais@psau.edu.sa; zahidkhan@hu.edu.pk

Abstract

This work presents a neutrosophic extension of the Fréchet distribution to enhance the modeling of extreme values under conditions of indeterminacy and uncertainty. While the classical Fréchet distribution is widely used in fields such as finance, hydrology, and environmental sciences to model extreme maximum values, it does not fully accommodate imprecise, vague, or conflicting data commonly encountered in real-world scenarios. By incorporating the principles of neutrosophic logic the proposed neutrosophic Fréchet distribution provides a more flexible and realistic approach to representing extreme phenomena. The paper introduces its theoretical formulation, outlines key statistical properties, and proposes an estimation method based on maximum likelihood. Through simulations and numerical illustrations, the robustness and applicability of the model are described, especially in contexts where data is incomplete, uncertain, or contradictory. A real industrial dataset is employed to illustrate the applicability of the proposed model.

Keywords: Probabilistic model; Neutrosophic probability; Neutrosophic measures; Estimation; Simulation