A gist that shows how a rootogram helps find that the zero-inflated negative binomial was the data generating mechanism.

rootograms.R

# install.packages("countreg", repos="http://R-Forge.R-project.org")
# https://www.fromthebottomoftheheap.net/2016/06/07/rootograms/
# https://channel9.msdn.com/Events/useR-international-R-User-conferences/useR-International-R-User-2017-Conference/countreg-Tools-for-count-data-regression
library(countreg)

rzinbinom(3e3, size = 4, mu = 20, pi = 0.05) -> x
table(x)
hist(x, col = "orange")

rootogram(glm(x ~ 1, family = "poisson")) # zeros under fit

rootogram(zeroinfl(x ~ 1, dist = "poisson")) # low counts under fit, high counts over fit

rootogram(zeroinfl(x ~ 1, dist = "negbin")) # zero fit well, low counts fit well, high counts fit well.

sort(ls("package:countreg"))