Large language models (LLM) are highly effective in generating human-like text but often produce hallucinations. These hallucinations occur when LLM tries to compensate for gaps in knowledge using strategies like contextual learning, probabilistic modeling, or fallback techniques. While these strategies enable the generation of plausible-sounding responses, they can also lead to incorrect or fabricated information. LLM uncertainty can be divided into two categories: epistemic uncertainty, caused by a lack of knowledge or data, and aleatoric uncertainty, which is due to inherent randomness in the data. Epistemic uncertainty is crucial for identifying hallucinations, as high levels indicate un- reliable or fabricated responses. However, current uncertainty quantification methods face challenges in distinguishing between these types of uncertainty, especially in scenarios with multiple possible responses. This work introduces a new method for quantifying LLM hallucinations by using negative nudging combined with a nonparametric statistical approach. By separating epistemic and aleatoric uncertainties, the method enhances hallucination detection, particularly when epistemic uncertainty is high. Through an information-theoretic metric based on mutual information, this approach provides more accurate uncertainty estimates, improving the reliability of LLM outputs. This method offers a significant improvement over traditional techniques, resulting in better uncertainty management and more reliable predictions in complex situations. The results of this type of quantification can be utilized in other concepts such as uncertainty of information for support decision making under uncertainty.