Modeling sales per day

What distribution would you chose to model the daily sales of a commercial entity?
Something like Amazon, Wall Mart Branch, etc…

The simplest model which it would make sense to sample from.
It should be supported on the non negative values.

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Counts are often modeled with Poisson or negative binomial distributions. So you might try those.


Or a discrete weibull if you have extreme daily/hourly sales, i.e. zero sales, 10 sales, or 6000 sales are possible as outcomes.


What about the revenue itself and not only the discrete number of sales?

It depends. If the revenue is summed over the # sales, depending on how large the number is you could get away with a normal/studentT distribution. But if you have transaction-level data with or small number of sales per day/part of day/or batch – and zero is not possible - you could use a gamma distribution. The choice of likelihood distribution is particular to what your data looks like. Even then, there could be competing distributions that fit your data, and you would need to fit and compare to see which mirrors your observed data best.


In my case the idea is just to generate data for testing. So a reasonable model would be great, it doesn’t have to fit a specific data.

Just like it will be reasonable to model proportion with Beta, I need something which makes sense in the context of generating data for simulation.

A lot depends on the data. If it’s daily then it’s plausible that there might be high levels of variance, and possibly zero inflation. As it is I think the question is a bit vague, so I’m sure that people can provide more suggestions if there’s a bit more to go on.

I know it is vague, hence I am not after being too accurate. Just reasonable.