The negative binomial distribution defines the probability of N draws to obtain K successes. The negative multinomial gives the joint over k1...km given k0 successes. I need to find the PMF over n given k failures OR successes (I.e. how many draws are needed to get either k failures or k succeses). Evetually I need to extend this to the multivariate case (how many draws do get k success in any of the urns).
Any help with the easier or harder problem will be much appreciated!