Bayes Estimator Under Neutrosophic Statistics: A Robust Approach for Handling Uncertainty and Imprecise Data

In this paper, we introduce a Bayes estimator that incorporates the loss function within the context of neutrosophic statistics. This novel estimator provides an alternative to the conventional Bayes estimator, particularly valuable for managing imprecise data and uncertainty. We utilize the proposed estimator to obtain the neutrosophic posterior distribution for the normal distribution. Additionally, an extensive simulation study and comparative analysis are conducted, demonstrating the significant impact of uncertainty on the mean, variance and posterior credible interval of the posterior distribution. Based on our findings, we advocate for the use of this Bayes estimator in uncertain environments across multiple fields.