Part of a model I am making includes the frequency with which people go shopping for a given good (e.g. people on average go to the supermarket some n times a month). I am trying to figure out what probability distribution is most appropriate for the task. I think that this can be modeled by a poisson process, because it involves a rate across time, but am unsure if occurrences of shopping are independent of each other in this case. I considered a normal distribution with the mean centered around some rate but am also unsure about that.
I think you were right with your initial consideration of Poisson. I think that you can assume that the frequency with which people go shopping for a given good can be considered independent. Of course this assumption might not be perfect (like maybe you could argue that Person A buys item X every 3 days. However, if there is enough people I don't think this should matter too much). Overall, sometimes I think if you need to use a distribution to approximate a process, you need to pick the best option and it seems like Poisson is best here.
Also, It can't be normal since its bounded (ie the lowest number of people that can go to a store is 0)