One major solution to detect outliers is the model-based method or statistical method. The outlier is defined as the object not belonging to the model that is used to represent the original dataset. In other words, that model does not generate the outlier.
Among the accurate models to be adopted for the specific dataset, there are many choices available such as Gaussian and Poisson. If the wrong model is used to detect outliers, the normal data point may wrongly be recognized as an outlier. In addition to applying the single distribution model, the mixture of distribution models is practical too.
The log-likelihood function is adopted to find the estimation of parameters of a model:
