I was trying to compare best fit model for monthly precipitation data sets and negative and positive infinity (-inf and inf) as values have showed up for both AIC and BIC tests. Can anyone tell me what that means? I am using it to compare which dataset has good fit for gamma distribution.

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  • $\begingroup$ AIC and BIC are information criteria, not tests. $\endgroup$ 2 days ago

It shows that something is wrong.

  • AIC is defined as $2k - 2\log \hat L$, so it would be infinite when the likelihood $\hat L$ is zero since $\log(0) = -\infty$. This would happen if the data has probability of zero or probability density of zero under the model. In such a case, your model is not appropriate for the data, since the data is considered to be impossible by the model.
  • Another possibility are numerical errors or bug in your code, so you need to do standard debugging.

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