In aquatic environments, autonomous robots equipped with environmental sensors play a pivotal role in gathering critical data to monitor and understand complex ecosystems. This research paper explores the modeling of signal variations generated by an aquatic robot submerged in water, considering factors such as temperature, pressure, salt content, and the number of living species in the surroundings. The primary focus is on characterizing and quantifying the random error inherent in the signal, with an emphasis on heavy-tailed probability distributions to account for extreme events and outliers. Various heavy-tailed distributions are examined in the context of their suitability to represent the distribution of errors in the robot’s signal. The research is conducted through extensive simulations enabling controlled experimentation and analysis of signal characteristics. AIC, BIC, K-S test for goodness of fit have been used to identify the best fitting distribution. This interdisciplinary research uses Mathematical Statistics to provide useful insights into the error dynamics of aquatic robots thus helping to improve their quality, consequently proving beneficial for various stakeholders which include, Engineers, Environmentalists, mathematicians, statisticians, and AI developers.