The Online Detection of Action Start (ODAS) has attracted the attention of researchers because of its practical applications in areas such as security and emergency response. However, online detection of activity boundaries remains a challenging task due to the inherent ambiguity of boundary definition and the significant imbalance in the number of boundaries and nonboundary points. To address this issue, this study proposes a novel Distribution-aware Activity Boundary Representation (DABR) method that utilizes a continuous probability density function to smooth the probability of moments near activity boundaries. The proposed DABR reduces the penalty for detecting moments near ground-truth boundary points, while increasing the number of samples related to boundary points. Additionally, we introduce a two-stage framework that incorporates class-informed information in temporal localization for more efficient activity boundary localization. Extensive experiments demonstrate that our method achieves state-of-the-art results on two standard datasets, particularly exhibiting a significant improvement of 11.5% at average p-mAP on the THUMOS'14 dataset.