I have training data that I have fitted with two types of Poisson models (one zero inflated and one standard) and I would like to compare each model's performance on a test set to see which one is better. How can I do this ? (I am using R if it makes a difference). I have already done chi-squared tests to determine that both fitted Poisson distributions are statistically significant with the training data.

Also, is there a standard way for testing the accuracy of a fitted probability distribution on a test set of data? E.g. like a mean-squared error reduction.

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    $\begingroup$ Some suggestions in this Q&A stats.stackexchange.com/questions/182020/… $\endgroup$
    – mdewey
    Jan 3, 2018 at 14:03
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    $\begingroup$ You might want to consider using a [quantile-quantile plot]() to see if your fitted probability distribution is a good fit. A good example is provided here $\endgroup$
    – slackline
    Oct 14, 2018 at 12:42