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I have a distribution of patient appointment booking time that looks like below. How can I simulate this data in excel? I am confused as to what distribution I should be using, it is not uniform or poisson.

enter image description here

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  • $\begingroup$ It likely doesn't belong to a parametric family. Maybe just simulate a mixture for poisson and call it good enough? $\endgroup$ – Demetri Pananos Apr 10 at 15:48
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    $\begingroup$ What is the goal of your simulation? Depending on what you are trying to accomplish, there are multiple different approaches. $\endgroup$ – Matthew Drury Apr 10 at 16:06
  • $\begingroup$ I'm trying to simulate data for an optimization problem, wherein I need to optimize patient no show rates at a clinic. I want to simulate this booking scenario, 7 to 19 here is the time of the day where patients have appointments $\endgroup$ – user3437212 Apr 10 at 16:57
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Based on your comment

I'm trying to simulate data for an optimization problem, wherein I need to optimize patient no show rates at a clinic. I want to simulate this booking scenario, 7 to 19 here is the time of the day where patients have appointments

I am assuming you want to generate a random set of appointments throughout the day that are typical of the activity historically seen at the clinic. If this is not the case then I will delete this answer.

One possible approach to achieving this is to sample directly from your historic data. Rather than explicitly defining a distribution to sample from. Under this approach, you should consider sampling whole days at a time rather than selecting individual appointments. This is because it seems unlikely to me that appointments throughout the day would be independent of each other as the clinician running the clinic is unlikely to schedule too many appointments in a short space of time.

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  • $\begingroup$ This makes perfect sense! Thank you very much $\endgroup$ – user3437212 Apr 10 at 18:19

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