How to define distribution by myself

I wonder how to define a dicrete distribution in stan.For instance,there is a distribution where P(y=1)=0.2,P(y=2)=0.3,P(y=3)=0.5. Thanks for any help!

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Is y an ordinal outcome?

If you have a fixed set of categories and you know the probabilities, then categorical is the distribution you are looking for. Note that in general to define a distribution, you need to provide the log-probability (for discrete distributions) or the log-density (for continuous distributions). So once you compute the probability, simply target += log(probability); will work (in fact that’s exactly what y ~ categorical(all_probabilities) will do).

Best of luck with your model!