Modeling Uncertainty in Healthcare Data Using the Neutrosophic Gamma-Lomax Distribution for Optimized Decision-Making

Mansour F. Yassen¹, Adnan Amin^2,*

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

²School of Economics, Beijing technology and business university, Beijing, China

Emails: mf.ali@psau.edu.sa; amin.adnan12@yahoo.com

Abstract

Healthcare data often involve uncertainty, imprecision, and partial information that are hardly handled by classical statistical models. Here, we propose a new generalization of the Gamma Lomax (GL) distribution under the neutrosophic environment, referred to as the neutrosophic Gamma Lomax (NGL) distribution, to overcome this drawback. In addition, the proposed model can be generalized to handle precise as well as uncertain healthcare data by incorporating neutrosophic logic including truth, falsity and indeterminacy. The classical properties of the Gamma-Lomax (GL) distribution are examined alongside their neutrosophic counterparts. Graphical representations, including density plots and associated reliability functions of the proposed model, are presented. The maximum likelihood estimation (MLE) is applied to find unknown parameters. The neutrosophic model is capable of modeling interval-valued results and uncertainties in practical data, and its effectiveness is verified by simulation studies and an illustration with infant mortality rates. The new method is conducive to the interpretability and credibility of statistical inference under uncertainty and is of high utility in health decision-making scenarios.

Keywords: Gamma model; Neutrosophic logic; Neutrosophic density; Neutrosophic estimation