Anomaly detection in sentiment analysis refers to detecting users' abnormal opinions, sentiment patterns or special temporal aspects of such patterns. Users' emotional state extracted from social media contains business information and business value for decision making. Social media platforms, such as Sina Weibo or Twitter, provide a vast source of information, which include user feedbacks, opinions and information on most issues. Many organizations also leverage social media platforms to publish information about events, products, services, policies and other topics frequently, analyzing social media data to identify abnormal events and make decisions in a timely manner is a beneficial topic. This paper adopts the multivariate Gauss distribution with the power-law distribution to model and analyze the users' emotion of micro-blogs and detect abnormal emotion state. With the measure of joint probability density value and the validation of the corpus, anomaly detection accuracy of individual user is 83.49\% and of different month is 87.84\% by this method. Through the distribution test, the results show that individual users' neutral, happy and sad emotions obey the normal distribution, but the surprised and angry emotions do not. Besides, emotions of micro-blogs released by groups obey power-law distribution, but the individual emotions do not. This paper proposes a quantitative method for abnormal emotion detection on social media, which automatically captures the correlation between different features of the emotions, and saves a certain amount of time by batch calculation of the joint probability density of data sets. The method can help the businesses and government organizations to make decisions according to the user's affective disposition, intervene early or adopt proper strategies if needed. (C) 2017 Elsevier B.V. All rights reserved.