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I have some data which contains anomalies as well.
I want to model data using Gaussian distribution assuming variables are dependent in Python.
How can I model this? Should I use the PDF formula as a function, figure out the probabilities and take out the accuracy?
Note: This has been given as an assignment in my college. I am trying to figure out the solution.
If you assume variables are dependent, in a Gaussian distribution this means the covariance matrix is not diagonal.
You can start with considering the multi-dimensional Gaussian distribution. Its density is $$ f(x_1,x_2,...,x_n) = \frac{1}{\sqrt{(2\pi)^n|\Sigma|}}\exp\left(-\frac{1}{2}(x - \mu)\Sigma^{-1}(x-\mu)\right)$$ (see https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Non-degenerate_case)
I suggest using the maximum likelihood approach to tune the parameters or any anomaly detection algorithm you know.
