Entropy estimation plays a crucial role in various fields, such as information theory, statistical data science, and machine learning. However, traditional entropy estimation methods often struggle with complex data distributions. Recently, mixture-based entropy estimation has been proposed and gained attention due to its ease of use and accuracy. This work proposes a novel approach based on the weighted likelihood bootstrap to quantify the uncertainty associated with mixture-based entropy estimation. Unlike standard methods, our approach leverages the underlying mixture structure by assigning random weights to observations in a weighted likelihood bootstrap procedure, leading to more accurate uncertainty estimation. The proposed approach is illustrated by analyzing the log-returns of Brent oil prices from NYMEX for the years 2014–2023. Quantifying the inherent randomness and its uncertainty offers valuable insights into the market’s resilience, volatility patterns, and potential future trends. This study not only advances uncertainty estimation in mixture-based entropy but also provides a unique perspective on the dynamics of the oil market, with potential implications for risk management and investment strategies.