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...Usually such behavior is not proficient to obtain good results, but this time I think that the change of prospective has been positive!
Approach based on Mutual Information
Before to explain my approach I have to say that I have not had time to check in literature if this method has been already implemented (please drop a comment if someone find out a reference! ... I don't want take improperly credits).
The aim of the method is to remove iteratively the sorted Z-Scores till the mutual information between the Z-Scores and the candidates outlier I(Z|outlier) increases.
At each step the candidate outlier is the Z-score having the highest absolute value.
Basically, respect the Chebyschev method, there is no pre-fixed threshold.
some comparative results: