I am struggling to find an appropriate distribution to model the total number of vacation days taken in a year.
I originally thought of going with a standard count distribution like negative binomial or even using hurdle regression to combine negbin with a logistic model. However, the nature of the dependent variable makes me second guess my choices.
The problem I have is that I am trying to predict the total number of days and these are not independent events. If I was modeling "# of vacations" and not days, I would be more willing to use a count model. I have searched all over for things like "duration modeling" but I am not finding anything helpful.
Any suggestions to point me in the right direction are greatly appreciated.