1. the overall distribution of progeny who are distributed normally about their randomly-distributed parents,
2. a random (Poisson) sum of logarithmic random variables
3. a Poisson mixture with a Gamma distribution,
4. a linear birth and death process,
5. a limit to the Polya distribution, a limit to the binomial mixture with the beta distribution,
6. the Polya birth process,
7. a population linear birth process,
8. a search-of-increasing area distribution,
9. the equilibrium case of a Markov chain,
10. a queuing process,
11. a waiting time distribution,
12. zero truncated, from a group-size distribution,
13. zero truncated, from a zero truncated Poisson mixture.

For full details see Boswell, M.T. & Patil, G.P. (1970). Chance mechanisms generating the negative binomial distributions. Random Counts in Scientific Work. e.d. G.P. Patil, 1:3-22. University Park, Pa: Pa. State Univ. Press