I am working with multivariate Gaussian distribution (MVG) to detect anomalies in time-series data. I have two features and thousands of observations. The first feature (left) has a very good normal distribution after applying "moving-averages" and Z-score normalization. However, the second feature has many zeroes and doesn't follow the normal distribution. Usually, my anomalies exist where feature-1 with a high score and feature-2 with a low score (especially zero). If it finds an outlier that has high scores in both features, it wouldn't call it. Because, in theory, MVG uses the covariance between feature1 and 2 and calls the predictions. Now my concerns are.
Feature-2 zeroes are important to find outliers and I don't want to remove them. If I don't, it violates the normal distribution assumption. What should I do in this case?
Also, in some rare cases where feature-1 and 2 have the highest scores, it detects outliers. Does it mean MVG is not working well or the first concern is somehow affecting how well the model works?