I have daily data of reservations for a restaurant with a certain capacity. I also know about the population size that will possibly visit this restaurant. I would like to do some analysis to get more insight into the demand for this restaurant.
I have been looking to model this using statistical methods, but encountered a few hurdles along the way looking for a framework. Because of seasonality, the number in the population of people possibly making a reservation differs (it ranges from ~100-500, but I do know exactly what this n is). I was looking at both binomial model, with each member of the population visiting with chance p, however the chance that one will visit is possibly dependent on other factors as well (weekday, season). Another option is to use a poisson model, but here too a struggle with the same questions as with the binomial data, as well as possibly having too small and each day differing size of population (I know that if n gets large and p is small the poisson is a limiting case of a binomial distribution)?
Also the restaurant reaches sometimes (especially in high season) it's capacity and reservations have to be rejected. For this I have been looking at truncation versus censoring. What is the difference between censoring and truncation? was helpful for this, and if I understand correctly, my data is (right) censored and not truncated. But I have difficulty in what to do know with this knowledge.
Do you have any tips in how to approach this two-fold problem? I was thinking to first "uncensoring" the data, but wouldn't know the best way to approach this. Much of the literature I found is on survival analysis, and I'm having difficulty translating this to the problem at hand.
