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stats newbie here.

I have a dataset that is collected weekly. In order to make sure the data set gathered this week conform to past observations, I'm using KL divergence to compute how similar the new data set is comparing to the previous one.

Imagine doing this process every week, I would eventually have a series of KL divergence data points. Is it possible to do anomaly detection through the distribution of these divergences?

My collection of KL divergences are skewed to the right, so usual normal/symmetric distribution methods doesn't quite work. I would like to be able to come up with a confidence level of how likely the new data set is an anomaly and how bad the anomaly is. I have looked around but haven't been able to find any specifics. Is it even possible to do what I want?

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