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I have a data set of 10000 obs of insurance claims. I've fitted it to a Gamma distribution after dividing my values by 10^8; to a Log-Normal distribution, without changing anything in my data set; and to a Normal distribution, by taking the natural log of all the values in my data set.

Now I need to pick the best model, and I want to use BIC values to justify my decision. But I feel like these values can't be compared due to the changes in my data set. Can I use BIC regardless of the changes?

The purpose of my analysis is simply deciding the best model for insurance claims.

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  • $\begingroup$ No, you can't choose your distribution based on information criteria. What is the purpose of your analysis? If you say more about your data, you might get some advice on how to proceed here. $\endgroup$
    – mkt
    Jul 11, 2019 at 18:58
  • $\begingroup$ IC can only be compared on the same data set, changing the data changes their values, so they are not comparable anymore. $\endgroup$ Jul 12, 2019 at 6:00

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Information criteria cannot be used to compare models fitted to different datasets (and by transforming values, you are changing the dataset).

But it's far from clear what type of model you are trying to fit or even what your goal is, since you only describe fitting distributions to the data - and no transformation is needed to do this.

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