Multinomial returns nan

Development
12

I would argue that a support of p=0, x=0 in the multinomial case implies a support of p=0, a=1 in the Dirichlet case. If f(x|p) is the multinomial distribution and f(p) is uniform on the simplex then by Bayes theorem

f(p|x) = \frac{f(x|p)f(p)}{f(x)} = f_{dirichlet}(p|a)

for a = x+1. Hence there should be support for a=1.

In particular for my application I need to draw from different Dirichlet distributions, all with the same shape, but sometimes a given category i has no members a_i=1. However one could achieve the same result by removing this category from the vector a and append p_i=0 to the result afterwards.

Scipy also does some other funny stuff. E.g. scipy.stats.lognorm.pdf(0, 1) returns 0.0 even know the definition includes a term 1/x and hence should not support x=0. Nevertheless this continuous continuation can be useful :slight_smile:

Edit: Corrected x_i=0 to p_i=0.