Identifying and addressing fraudulent activities that deviate from expected patterns is a vital part of customer relationship management (CRM) and financial security in the finance industry. Given the ever-changing landscape of fraud tactics, it can be challenging for traditional detection systems to keep up, especially when it comes to analyzing the intricate and multi-faceted nature of transaction data. This study presents a complex model that utilizes a multivariate normal distribution to accurately distinguish between valid and fraudulent transactions. The method utilizes a multivariate normal distribution that is based on specific features extracted from a dataset of credit card transactions. This allows for the modeling of genuine transaction behavior. The model’s threshold is dynamically adjusted and optimized using a probability distribution created from real transaction data, allowing for accurate detection of anomalies. The optimization of this threshold is critically guided by the F2-score, which focuses on minimizing false negatives in situations where undetected fraud can lead to significant financial losses. We employ a comprehensive approach that involves meticulous data preprocessing, creative feature engineering, and meticulous evaluation of the model. We place a strong emphasis on identifying the distinguishing characteristics that separate fraudulent transactions from legitimate ones, thereby enhancing our ability to accurately detect fraudulent activity. We conducted a thorough evaluation of the system’s performance using a real-world dataset. The results showed a remarkable accuracy of 99.6%, indicating a strong ability to make correct predictions. Additionally, the precision was measured at 79.8% and the recall at 82.1%, further highlighting the system’s effectiveness. The F2-score, which measures the model’s accuracy in identifying frauds, was impressively high at 81.6%. This research makes significant contributions to the field of anomaly detection within CRM systems, leading to advancements in fraud detection capabilities. As a result, it promotes enhanced consumer security and trust, both in theory and in practice.