Outlier detection aims to detect those data that significantly deviate from the expected behavior, and thus is widely applied in many fields, such as, machine fault detection, intrusion detection, fraud detection and data preprocessing. Hence, there exist many generic and special algorithms for outlier detection under the unsupervised and supervised learning framework. But up to now, there still has been no clear classification in this aspect. To provide a structural view, the review of the state-of-the-art statistics-based methods for outlier detection was focusedon, and a simple classification was given in this aspect. Moreover,the equivalence between some outlier detectors in depth is particularly discussed.