I am trying to simulate a user that generates files over a whole year. I have a dataset with information about date and time of files generated from a user and it follows negative binomial distribution. I need to model inter arrival time. I have two possible approaches and I need advice on choosing one.
My first question is related to first arrival, especially for days with one file generated (any reference is welcome) Many examples I find online assume that the first event happened at time 0, but this is not correct in my case. There are examples that say that the time interval (24h) should be divided into fixed time interval where there is no arrival in first one.
When I model inter arrival times should I
- take all Mondays (52 during a year) and calculate inter arrival times for every hours and then calculate the probability that files will be generated in that hours.
- treat all days equally and then do the same thing (for every hour) for all days. After I grouped data based on hours I created this table that shows some peaks:
Or maybe some other approach is better; any advice is welcome.