Distribution for the number of sales per day / time between each sale [migrated]

Solution 1:

The (time) points of sales can be modeled as a point-process, and the simplest model is a Poisson point process. You also seem to be assuming a homogeneous process, that is, with an intensity function that do not vary with time. But the Poisson process assumes the events (sales) are independent, and, for example, the same customer making multiple buys close in time would violate that. So you should also look into more general point process models. See for instance Point Pattern Analysis- what is it good for.

But, if you have a Poisson point process, the time between events will have an exponential distribution. So a practical way of testing the Poisson assumption is to check if the waiting times do have an exponential distribution!

As for your additional question in comment, you have an inhomogeneous Poisson process, there is some information at

• How to estimate Poisson process using R? (Or: how to use NHPoisson package?)

• Estimating Poisson process intensity using GLM

• Renewal process vs inhomogeneous Poisson process?