I have been trying to help a friend come up with sales projections for a potential project using pretty standard industry data and regression modeling. I was thinking it would be interesting to model actual customer behavior at the hourly / daily level.
I was think the daily counts could be modeled by non-homogenous Poisson Process with the rate varying across lunch peak and nighttime sales. I would then like to be able to model number of pints and beer and food sold given some kind of distribution. Then I could run some simulations.
I keep thinking all the random variables are Poisson, but I think there is more to it.
First, I would have the number of customers per day as N ~ Poisson(u0) and then estimate the number brews and food dishes an individual has by modeling them either Binomial or Poisson random variables. This is where I am confused, I am not sure how to model the number of brews and food customers purchase on average. I know given a Poisson number of customers and if the number of beers purchased is binomial then I can model this situation with a Poisson distribution with parameter lambda*p, but I am not sure how to model beers and food while including the situation that an individual gets both. Would I use a Multinomial distribution conditioned on the same Poisson variable?
Not sure what the approach this type of problem is.
I know my thoughts are pretty scattered as I have not studied this stuff for many years, but I would like to research this further. If anything, can anyone point me to any literature with similar types of problems? I have a good probability modeling book, but there are not many numeric examples.
Any help would be appreciated.