The primary focus of this research is to explore the incorporation of an inherently stochastic Poisson-inspired kernel function into Support Vector Machines (SVMs) to detect Distributed Denial of Service (DDoS) attacks. The study focuses on assessing the performance of the Poisson kernel in comparison to established SVM kernels, including Linear, Polynomial, and Radial Basis Functions (RBF). The Poisson kernel was chosen for DDoS attack detection due to the stochastic nature of DDoS attacks, which align well with the characteristics of the Poisson distribution. This research hypothesizes that the efficiency of the Poisson kernel within SVM can considerably improve its capacity to uncover hidden patterns in DDoS attack data. Thorough testing and analysis, reveals the Poisson kernel's competitive edge, showcasing impressive accuracy and a distinctive ability to handle non-linear data. The kernel's balanced approach in minimizing false positives and false negatives positions is valuable for challenging categorization tasks. However, careful hyperparameter optimization is essential, and challenges may arise in high-dimensional datasets. These limitations contribute to the broader discourse in machine learning, offering insights for future research. The paper contributes to the constant evolution of machine learning solutions, presenting the Poisson kernel as a promising innovation in DDoS attack detection. As classification tasks gain significance across various sectors, the Poisson kernel emerges as a versatile and refined solution with the potential for ongoing growth and optimization.