This project investigates whether customer arrivals to digital healthcare providers can be appropriately modeled by non-homogeneous Poisson processes (NHPPs).
Data from a large Swedish telemedicine provider was examined, with the goal of confirming that the data exhibited the two required properties of Poisson processes: customer interarrival times being (i) exponentially distributed, and (ii) independently and identically distributed. The arrival process was modeled as a piecewise constant arrival function, with several interval lengths considered. Two statistical tests were performed, the Kolmogorov-Smirnov and Brock-Dechert-Scheinkman tests, to confirm whether the two properties held.
The experiments showed that a majority of intervals exhibited both properties, suggesting that NHPPs are a useful approach for modeling telemedicine customer arrival data.