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Just a note

These models are:
  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