Truncated multinomial and dirichlet-multinoial

[Ara_Winter]

Maybe not quite what you are looking for but:

Constraining Output of Multinomial Distribution

I have a general question regarding constraining the output of a multinomial regression. Assume the model is as follows: we have 5 types of fruit, each having N_k, k = 1,\ldots,5 pieces to choose from. If I select N total pieces of fruit, I would like to model how many of each fruit I am going to choose. For this, I am going to use a Multinomial distribution. The issue is, at each “time-step” I can only choose a maximum of N_k of the k th type of fruit. Since I know N_k for each time-step, …