In marketing, people assume that individual customer purchases are distributed according to a poisson distribution. This may be an incorrect assumption, however all models are wrong but some are useful.
I've managed to find some customer transaction data
housing that contains the customer ID and date of purchase as rows for several thousand customers (available here). Here is a sample of the data:
CustomerID InvoiceDate 17381.0 2011-10-04 08:30:00 15749.0 2011-04-18 13:08:00 14371.0 2011-02-17 16:35:00 18226.0 2011-07-03 10:47:00 14012.0 2011-03-07 12:26:00 13144.0 2011-01-11 11:15:00 12852.0 2011-02-18 08:47:00 12901.0 2011-06-23 16:00:00 13854.0 2011-03-21 11:20:00 13158.0 2011-01-25 09:58:00
The data is publicly available, so I don't think there are any issues posting it here.
I can group the customers and count their transactions for any period of time. I'd like to check how well this assumption of being poisson distributed is.
Could I just count the transactions for a given customer weekly, and then use the chi-square goodness of fit test to determine if the data could have been distributed according to a poisson distribution? Am I missing something crucial in my assumptions?