I blame Rully for this. If it wasn’t for him I wouldn’t have been obsessed with this and spent a good few hours at night figuring it out last week. It all started when Rully mentioned that he knew how many beeps there are in the Singapore MRT (subway system) ‘doors closing’ warning. There are 

Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).