These models are:
- the overall distribution of progeny who are distributed normally about their randomly-distributed parents,
- a random (Poisson) sum of logarithmic random variables
- a Poisson mixture with a Gamma distribution,
- a linear birth and death process,
- a limit to the Polya distribution,
a limit to the binomial mixture with the beta distribution,
- the Polya birth process,
- a population linear birth process,
- a search-of-increasing area distribution,
- the equilibrium case of a Markov chain,
- a queuing process,
- a waiting time distribution,
- zero truncated, from a group-size distribution,
- 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