The Neutrosophic New XLindley Distribution: Statistical Properties, Estimation, Simulation, and Application

This paper introduces a novel framework for deriving neutrosophic credibility bounds within the context of the Neutrosophic New X-Lindley Distribution (NNXLD), an extension of the classical X-Lindley dis tribution that integrates indeterminate and imprecise information. The main focus is to construct neutrosophic Bayes estimators and contrast their performance with classical Bayesian estimators, highlighting the enhanced f lexibility offered in modeling uncertainty. The methodology includes the derivation of statistical properties of the NNXLD and the implementation of three estimation techniques—Maximum Likelihood Estimation (MLE), Method of Moments (MoM), and Bayesian estimation under a Gamma prior. A simulation study evaluates the estimators’ accuracy using bias, mean squared error, and standard deviation across varying sample sizes. Furthermore, the model’s real-world relevance is illustrated through an application to insurance claim severity data, demonstrating its robust fit in the presence of uncertainty. The results confirm the practical advantages of neutrosophic modeling in handling vague, incomplete, or subjective data, making the NNXLD a valuable tool in reliability and actuarial science.